Exponent Laws Quiz
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Exponent Laws Quiz

Test your understanding of the exponent laws, including the product of powers, power of a power, power of a product, quotient of powers, zero exponent, and negative exponent. Practice applying these laws to simplify exponential expressions and solve problems.

Created by
@UnbiasedGreatWallOfChina

Questions and Answers

What is the result of (2^3 × 2^4)?

2^7

Simplify the expression (3^2)^4.

3^8

What is the result of (2^3 × 3^3)^2?

2^6 × 3^6

Simplify the expression 2^5 ÷ 2^3.

<p>2^2</p> Signup and view all the answers

What is the value of a^(-2) in terms of a?

<p>1/a^2</p> Signup and view all the answers

What is the result of (a^3 b^2)^4?

<p>a^12 b^8</p> Signup and view all the answers

What is the result of a^5 × a^(-3)?

<p>a^2</p> Signup and view all the answers

What is the result of (a^2 b^3) × (a^4 b^2)?

<p>a^6 b^5</p> Signup and view all the answers

What is the result of a^3 ÷ a^(-2)?

<p>a^5</p> Signup and view all the answers

What is the result of (a^2)^3 × (a^3)^2?

<p>a^13</p> Signup and view all the answers

Study Notes

Exponent Laws

Product of Powers

  • Law: a^m × a^n = a^(m+n)
  • When multiplying two exponential expressions with the same base, add the exponents

Power of a Power

  • Law: (a^m)^n = a^(mn)
  • When raising an exponential expression to a power, multiply the exponents

Power of a Product

  • Law: (ab)^m = a^m × b^m
  • When raising a product of two bases to a power, raise each base to that power and multiply

Quotient of Powers

  • Law: a^m ÷ a^n = a^(m-n)
  • When dividing two exponential expressions with the same base, subtract the exponents

Zero Exponent

  • Law: a^0 = 1
  • Any base raised to the power of 0 is equal to 1

Negative Exponent

  • Law: a^(-n) = 1/a^n
  • A negative exponent is equivalent to the reciprocal of the positive exponent

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