Question

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

left parenthesis 7 superscript 8 baseline right parenthesis times left parenthesis 7 superscript 10 baseline right parenthesis

left parenthesis negative 5 right parenthesis superscript 0 baseline


left parenthesis 7 superscript 4 baseline right parenthesis superscript 8 baseline
12^9

Answer 1

The Power Rule of Exponents states that \((a^m)^n = a^{m \cdot n}\). To identify which of the provided expressions is correctly developed to use this rule, let's analyze each one:

1. \((7^8) \times (7^{10})\) - This expression does not use the Power Rule but rather the Product of Powers Rule, which states \(a^m \times a^n = a^{m+n}\).

2. \((-5)^0\) - According to the Zero Exponent Rule, any non-zero base raised to the power of 0 equals 1, but it doesn't illustrate the use of the Power Rule.

3. \((7^4)^8\) - This expression uses the Power Rule of Exponents, and can be calculated as \(7^{4 \cdot 8} = 7^{32}\).

4. \(12^9\) - This is just a single power expression and does not illustrate the use of the Power Rule.

The correct expression that illustrates the Power Rule of Exponents is:

\((7^4)^8\)