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

Hello!

The answer are:

- Product of powers.

- Power of a power.

- Negative exponents.

Let's solve it!

It's a math rule that we must solve first what's into a brake or parenthesis, so,

First: Product of powers

According to the exponent's law, we have a product of powers case, so, we need to sum the exponents and keep the base

Exponents: 5 and 3

Base: 7

Applying it we have:

Then,

We have a power of a power case, which involves multiplying the exponents:

Exponents: 3 and -4

Then,

Finally, we can apply the negative exponents, the negative exponent's rules state that negative exponents are the reciprocal of the positive exponents,

So, we will have that:

Have a nice day!

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

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step-by-step explanation:

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