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 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:

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

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