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

Question

Responses

(−5)0
left parenthesis negative 5 right parenthesis superscript 0 baseline

(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

Answer 1

To correctly develop an expression using the Power Rule of Exponents, we want to look for an expression that can be simplified using the rule, which states that \(a^m \cdot a^n = a^{m+n}\) and \((a^m)^n = a^{m \cdot n}\).

1. ((-5)^0: This expression simplifies to 1, but it does not involve application of the power rule.

2. ((7^8) \cdot (7^{10}): Here, we can apply the power rule. The exponents can be added together because the bases are the same: \[ 7^8 \cdot 7^{10} = 7^{8+10} = 7^{18} \]

3. (12^9: This expression does not involve any operation between exponents and cannot be simplified further using the power rule.

4. ((7^4)^8: This expression can use the power rule where we multiply the exponents: \[ (7^4)^8 = 7^{4 \cdot 8} = 7^{32} \]

From the options, the expression that is correctly developed using the Power Rule of Exponents is ((7^8) \cdot (7^{10}).