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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

2^7

3^8

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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