Exponent properties review (article) | Khan Academy (2024)

Review the common properties of exponents that allow us to rewrite powers in different ways. For example, x²⋅x³ can be written as x⁵.

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  • janana

    7 years agoPosted 7 years ago. Direct link to janana's post “I'm confused by the fact ...”

    I'm confused by the fact that all exponents to the 0th power equals 1. Why is this? Shouldn't the answer be zero instead?

    (38 votes)

    • Hosannah H

      7 years agoPosted 7 years ago. Direct link to Hosannah H's post “When you look at it, not ...”

      Exponent properties review (article) | Khan Academy (4)

      Exponent properties review (article) | Khan Academy (5)

      Exponent properties review (article) | Khan Academy (6)

      When you look at it, not really. Let's pick a small number: 2
      2 to the power of 4=16
      2 to the power of 3=8
      2 to the power of 2=4
      2 to the power of 1=2
      Now when you look at these numbers, you should notice a pattern. 8/2=4, and 4/2=2. Now 2 divided by 2 would give us the answer to 2 to the power of 0, which is equal to 1.

      Hope that you understand now. Good luck!!

      (189 votes)

  • 25jevel289

    4 years agoPosted 4 years ago. Direct link to 25jevel289's post “who added letters in math...”

    who added letters in math i would like to have a conversation with them please

    (62 votes)

    • Mikeala

      a year agoPosted a year ago. Direct link to Mikeala's post “François Viète is the per...”

      Exponent properties review (article) | Khan Academy (10)

      Exponent properties review (article) | Khan Academy (11)

      François Viète is the person you should speak to about adding numbers to math.
      At the end of the 16th century, François Viète introduced the idea of representing known and unknown numbers by letters, nowadays called variables, and the idea of computing with them as if they were numbers—in order to obtain the result by a simple replacement.

      (26 votes)

  • Gabriel Zubovsky

    6 years agoPosted 6 years ago. Direct link to Gabriel Zubovsky's post “What's 0 to the 0th power...”

    What's 0 to the 0th power ?

    (32 votes)

    • Lovish Garg

      3 years agoPosted 3 years ago. Direct link to Lovish Garg's post “Well it will be undefined...”

      Exponent properties review (article) | Khan Academy (15)

      Exponent properties review (article) | Khan Academy (16)

      Well it will be undefined. See this case
      2^3=2*2*2 =8
      2^2=2*2 =4
      2^1=2 =2
      2^0=1
      The reason we get 2^0 is because for every 2^{n-1}, we are dividing the 2^n by 2, for example to get value of 2^0, we are dividing the 2^1=2 by the 2. The result is therefor 1.

      But in case of 0, we will be dividing the 0 by the 0. Because 0^1=0 and then we will be diving by our base (which is 0), the result will be 0/0, which is undefined.
      I hope you got my point.
      Have a nice day.

      (34 votes)

  • Victoria563

    4 years agoPosted 4 years ago. Direct link to Victoria563's post “Can an exponent have an e...”

    Can an exponent have an exponent?

    (21 votes)

    • THE BETTER WINCHESTER

      3 years agoPosted 3 years ago. Direct link to THE BETTER WINCHESTER's post “Of course! It's mostly se...”

      Exponent properties review (article) | Khan Academy (20)

      Exponent properties review (article) | Khan Academy (21)

      Of course! It's mostly seen in this form, though: (4^2)^3 where there is one exponent inside the parenthesis then outside the parenthesis there's another exponent, which applies to all parts inside the parenthesis, including the exponent inside.

      (25 votes)

  • izayah

    2 years agoPosted 2 years ago. Direct link to izayah's post “i wish we can go back to ...”

    i wish we can go back to 1+1 and 2+2

    (33 votes)

    • RAIDA YESSIN

      a year agoPosted a year ago. Direct link to RAIDA YESSIN's post “If you still using them d...”

      If you still using them don’t worry but to survive in this digital era and going to Mars you will need those more complicated mathematical expressions and equations to solve your everyday problems and you may solve one of the world problems one day you never know. My humble advice to anyone who is taking mathematics is to start from beginning and build up at your own pace so you can perceive it better and have as many examples as possible also research what you can't understand and try to solve as many problems as you can

      (6 votes)

  • kabeeralimuhammad11

    a year agoPosted a year ago. Direct link to kabeeralimuhammad11's post “I am using Khan Academy f...”

    I am using Khan Academy first time. Khan Academy teaches very Amazingly.

    (32 votes)

  • hyost

    a year agoPosted a year ago. Direct link to hyost's post “this is way to easy! I ha...”

    this is way to easy! I have alr learned this and my mamma is making me do this :(

    (17 votes)

  • TheJester(lauren)

    a year agoPosted a year ago. Direct link to TheJester(lauren)'s post “Why do we have to learn a...”

    Why do we have to learn all of this??

    (5 votes)

    • Jasmine K

      a year agoPosted a year ago. Direct link to Jasmine K's post “You never know when this ...”

      Exponent properties review (article) | Khan Academy (32)

      You never know when this might come up in life. Sometimes, it forms the border between getting accepted into your college, or getting a good grade on a test.

      Wish you luck on whatever you're learning!

      (17 votes)

  • dsnider

    8 years agoPosted 8 years ago. Direct link to dsnider's post “Is there an answer to x^3...”

    Is there an answer to x^3 without "x" being part of the answer?

    (5 votes)

    • Kim Seidel

      8 years agoPosted 8 years ago. Direct link to Kim Seidel's post “The only way you can get ...”

      Exponent properties review (article) | Khan Academy (36)

      The only way you can get an answer for x^3 without have "x" be part of the answer is if you know the value of "x". For example, if someone says x=4, then we can find x^3.
      x^3 = 4^3 = 64. Otherwise, you are stuck with the "x".

      (15 votes)

  • Montilla, Andrea

    4 years agoPosted 4 years ago. Direct link to Montilla, Andrea's post “can an exponent have an e...”

    can an exponent have an exponent

    (6 votes)

    • 50024

      3 years agoPosted 3 years ago. Direct link to 50024's post “Of course! It's mostly se...”

      Of course! It's mostly seen in this form, though: (4^2)^3 where there is one exponent inside the parenthesis then outside the parenthesis there's another exponent, which applies to all parts inside the parenthesis, including the exponent inside.

      (7 votes)

Exponent properties review (article) | Khan Academy (2024)

FAQs

How to do property of exponents? ›

To simplify expressions with exponents, there are a few properties that may help. One is that when two numbers with the same base are multiplied, the exponents can be added. Another is that when a number with an exponent is raised to another exponent, the exponents can be multiplied.

What is the product of powers property? ›

The product of powers property tells that different bases raised to the same power can be grouped in a product that will be raised to that power. It also tells that the product between two powers of the same base will maintain the base and sum the exponents of the powers being multiplied.

What are the rules for multiplication of exponents? ›

When multiplying like bases, keep the base the same and add the exponents. When raising a base with a power to another power, keep the base the same and multiply the exponents. When dividing like bases, keep the base the same and subtract the denominator exponent from the numerator exponent.

What is the exponent trick? ›

The exponent rules are: Product of powers rule — Add powers together when multiplying like bases. Quotient of powers rule — Subtract powers when dividing like bases. Power of powers rule — Multiply powers together when raising a power by another exponent.

How do you calculate exponents easily? ›

If n is a positive integer and x is any real number, then xn corresponds to repeated multiplication xn=x×x×⋯×x⏟n times. We can call this “x raised to the power of n,” “x to the power of n,” or simply “x to the n.” Here, x is the base and n is the exponent or the power.

What are the 7 rules for exponents laws of exponents? ›

  • Zero property: a^0 = 1.
  • Product property: (a^x)(a^y) = a^(x + y)
  • Quotient property: a^x /a^y = a^(x - y)
  • Negative property: a^(-x) = 1 / a^x.
  • Power of a power: (a^x)^y = a^(x * y)
  • Power of a product: (ab)^x = (a^x)(b^x)
  • Power of a quotient: (a/b)^x = a^x / b^x.
May 6, 2020

What is the formula for exponential properties? ›

An exponential function is a mathematical function of the form f(x) = a.bx, where: 'a' is constant term known as the coefficient, 'b' is the base of the exponential function, which is a positive constant, and 'x' represents the exponent, which can be any real number.

What is the zero exponent rule? ›

The zero exponent rule simply states that any nonzero number raised to the power of 0 is equal to 1. The Zero Exponent Rule. a 0 = 1 , a ≠ 0. 0 0 is considered undefined. The zero exponent rule is sometimes referred to as the zero exponent property, zero exponent definition, or zero power rule.

What is the negative exponent rule? ›

The negative exponent rule states that the base must be written as its reciprocal, and then the exponent will become positive. 10 to the negative power of 2 is rewritten as 1/10 to the power of 2. 10 to the power of 2 is 100, so 10 to the negative power of 2 is 1/100.

How do you solve power property? ›

This is called the power of a power property and says that to find a power of a power you just have to multiply the exponents.

How do you find the answer in exponential form? ›

A number in exponential form is written by taking the base number used as a factor multiple times, and raising it to the power of the number of times it is used as a factor, for example, 3 to the fourth power is 3x3x3x3, or 3 multiplied by itself four times.

How do you solve an equation for an exponent? ›

Rewrite each side in the equation as a power with a common base. Use the rules of exponents to simplify, if necessary, so that the resulting equation has the form bS=bT b S = b T . Use the one-to-one property to set the exponents equal to each other. Solve the resulting equation, S = T, for the unknown.

How to find a variable that is an exponent? ›

The simplest way to solve that is to take the log_a (logarithm base a) of both sides. log_a(a^x) = x is an identity which allows you to bring the variable out of the exponent. In the case a^x = c, you're left with x = log_a(c). And you can either leave it like that or plug it into a calculator for approximation.

References

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