Which expression is correctly developed to use the Power Rule of Exponents?(1 point)

Question

Responses

(78)⋅(710)
left parenthesis 7 superscript 8 baseline right parenthesis times left parenthesis 7 superscript 10 baseline right parenthesis

129
12 superscript 9 baseline

(74)8
left parenthesis 7 superscript 4 baseline right parenthesis superscript 8 baseline

(−5)0

Answer 1

To identify which expression can be correctly developed using the Power Rule of Exponents, let’s examine each option:

1. (78)⋅(710): This can be expressed as \(7^8 \cdot 7^{10}\). According to the Power Rule, when multiplying like bases, we add the exponents: \(7^{8+10} = 7^{18}\). This expression is a valid use of the Power Rule.

2. 129: This does not apply as it does not involve exponents.

3. (74)8: This should be interpreted as \((7^4)^8\). According to the Power Rule, when raising a power to another power, we multiply the exponents: \((7^4)^8 = 7^{4 \cdot 8} = 7^{32}\). This also is valid.

4. (−5)0: This evaluates to 1 (since any non-zero number raised to the power of 0 equals 1), but does not demonstrate a use of the Power Rule as it doesn't involve combining exponents.

The expressions that correctly use the Power Rule of Exponents are:

• (78)⋅(710) resulting in \( 7^{18} \)
• (74)8 resulting in \( 7^{32} \)

So, both the first and the third options are valid applications of the Power Rule. If you need to select just one, choose (78)⋅(710), as it explicitly shows the multiplication of exponents.