Question

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

Answer 1

Answer:

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

Answer 2

Answer:

-Product of powers.

-Power of powers.

-Negative exponent.

-Power of a product.

Step-by-step 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:

$\frac{1}{(7^{8})^{4}}$

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

$\frac{1}{7^{32}}$

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.