Laws of Exponents

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What is the Product of Powers Property?

When multiplying two exponents with the same base, you add the exponents.

How can the Power of a Power Property be described?

When raising a power to another power, you multiply the exponents.

What does the Quotient of Powers Property state?

When dividing two exponents with the same base, you subtract the exponents.

How is the Zero Exponent Rule defined?

Any non-zero base raised to the power of zero is equal to one.

What happens when you apply the Negative Exponent Rule?

A negative exponent indicates taking the reciprocal of the base and then applying the positive exponent.

Explain the Power of a Product Property.

Distribute the exponent to each factor inside the parentheses.

What is the Power of a Quotient Property?

Distribute the exponent to both the numerator and the denominator of the fraction.

If you have a base of 5 with an exponent of -3, how do you simplify it?

1/5^3, or 1/125.

How do you express (3^2)^3 using the Power of a Power Property?

3^6.

What is the simplified form of 2^3 * 2^4?

2^7.

How do you simplify 10^5 / 10^2 using the Quotient of Powers Property?

10^3.

What does 7^0 equal?

1.

Simplify 4^-2 using the Negative Exponent Rule.

1/16.

How do you apply the Power of a Product Property to (3 * 2)^4?

3^4 * 2^4.

What is the result of applying the Power of a Quotient Property to (2/3)^3?

2^3/3^3.




Test Your Knowledge

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1. What is the Product of Powers Property?

When multiplying two exponents with the same base, you add the exponents.

When dividing two exponents with the same base, you subtract the exponents.

Any non-zero base raised to the power of zero is equal to one.

2. How can the Power of a Power Property be described?

Distribute the exponent to each factor inside the parentheses.

When raising a power to another power, you multiply the exponents.

When multiplying two exponents with the same base, you add the exponents.

3. What does the Quotient of Powers Property state?

When dividing two exponents with the same base, you subtract the exponents.

When multiplying two exponents with the same base, you add the exponents.

A negative exponent indicates taking the reciprocal of the base and then applying the positive exponent.

4. How is the Zero Exponent Rule defined?

Any non-zero base raised to the power of zero is equal to one.

When raising a power to another power, you multiply the exponents.

A negative exponent indicates taking the reciprocal of the base and then applying the positive exponent.

5. What happens when you apply the Negative Exponent Rule?

A negative exponent indicates taking the reciprocal of the base and then applying the positive exponent.

Distribute the exponent to each factor inside the parentheses.

When multiplying two exponents with the same base, you add the exponents.

6. Explain the Power of a Product Property.

Distribute the exponent to each factor inside the parentheses.

Distribute the exponent to both the numerator and the denominator of the fraction.

When dividing two exponents with the same base, you subtract the exponents.

7. What is the Power of a Quotient Property?

A negative exponent indicates taking the reciprocal of the base and then applying the positive exponent.

Distribute the exponent to both the numerator and the denominator of the fraction.

When multiplying two exponents with the same base, you add the exponents.

8. If you have a base of 5 with an exponent of -3, how do you simplify it?

1/5^3, or 1/125.

5^3, or 125.

25.

9. How do you express (3^2)^3 using the Power of a Power Property?

3^6.

(3^2)^5.

3^5.

10. What is the simplified form of 2^3 * 2^4?

2^7.

2^12.

2^5.

11. How do you simplify 10^5 / 10^2 using the Quotient of Powers Property?

10^3.

10^7.

10^2.

12. What does 7^0 equal?

1.

7.

0.

13. Simplify 4^-2 using the Negative Exponent Rule.

1/16.

16.

4.

14. How do you apply the Power of a Product Property to (3 * 2)^4?

3^4 * 2^4.

3^2 * 2^2.

(3^4)^2.

15. What is the result of applying the Power of a Quotient Property to (2/3)^3?

2^3/3^3.

2^2/3^2.

2^3/3.