Question

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

Answer 1

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 a brake or parenthesis, so,

First: Product of powers $[(7)^{5}*(7)^{3}]$

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:

$(7)^{5+3}$

$(7)^{8}$

Then,

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

$[(7)^{5}*(7)^{3}]^{-4}$

Exponents: 3 and -4

Then,

$(7)^{8*-4}$

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:

$(7)^{-32}=\frac{1}{7^{32} }$

Have a nice day!

Answer 2

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