Question

Which rules of exponents will be used to evaluate the expression. Check all that apply

Answer 1

-Product of powers.

-Power of powers.

-Negative exponent.

-Power of a product.

Explanation:

1. According to the product of powers, when you have two powers with equal base you must sum the exponents. Then you have:

`[(7^(5))(7^(3))]^(-4)=[7^(8)]^(-4)`

2. The negative exponents indicates that 7⁸ is in the denominator. Based on this, you have:

`(1)/((7^(8))^(4))`

3. Based on the power of powers, you can multiply the exponents. Then:

`(1)/(7^(32))`

You can also apply the power of a product:

`[(7^((5)(-4)))(7^((3)(-4)))]=[7^(-20)*7^(-12)]`

And then apply the step 2.

Answer 2

Three rules are used

1) Product of powers

2) Power of a power

3) Negative exponents

Step-by-step explanation:

The given expression is [(7)⁵(7)³]⁻⁴

To find the value of [(7)⁵(7)³]⁻⁴

[(7)⁵(7)³]⁻⁴ = [(7)⁵⁺³]⁻⁴ = [(7)⁸]⁻⁴(using product of powers rule)

[(7)⁵⁺³]⁻⁴ = [(7)⁸ˣ⁻⁴] = 7⁻³² [using powers of power rule)

7⁻³² = 1/7³² (using negative exponent rule)

Using three rules we can solve [(7)⁵(7)³]⁻⁴

Therefore the correct answers are

1) Product of powers

2) Power of a power

3) Negative exponents