Question

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

Answer 1

Three rules are used

1) Product of powers

2) Power of a power

3) Negative exponents

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

Hello!

The answer are:

- Product of powers.

- Power of a power.

- Negative exponents.

Why?

Let's solve it!

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

First: Product of powers
`[(7)^(5)*(7)^(3)]`

According to the exponent's law(produc of power property)we need to sum the exponents and keep the base

Exponents: 5 and 3

Base: 7

Applying it we have:

`(7)^(5+3)=(7)^(8)`

Then, we can apply the power of a power property.

The power of a power property state that we must keep the same base and then multiply the exponents:

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

Exponents are:

3

-4

So,

`(7)^(8*-4)=(7)^(-32)`

Finally, we apply the negative exponents property, negative exponents are the reciprocal of the positive exponents,

So, we will have that:

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

Have a nice day!