Question

Which expression is correctly developed to use the power rule of exponents?

(7^4)^8
(-5)^0
(7^8)*(7^10)
12^9

Answer 1

To identify which expression correctly uses the power rule of exponents, let's briefly review the power rule. The power rule states that \( (a^m)^n = a^{m \cdot n} \).

Now, let's evaluate each expression:

1. **\((7^4)^8\)**:
- This can be expressed using the power rule:
\[
(7^4)^8 = 7^{4 \cdot 8} = 7^{32}
\]
- This is a correct application of the power rule.

2. **\((-5)^0\)**:
- Any non-zero number raised to the power of 0 is 1, which is not directly an application of the power rule but rather a property of exponents.
- This doesn't utilize the power rule.

3. **\((7^8) \cdot (7^{10})\)**:
- This can be combined using the property of exponents:
\[
7^8 \cdot 7^{10} = 7^{8+10} = 7^{18}
\]
- This expression makes use of the property of exponents but does not specifically utilize the power rule.

4. **\(12^9\)**:
- This expression is simply in exponential form and does not employ any exponent rules.

Based on this analysis, the expression **\((7^4)^8\)** is the one that is correctly developed to use the power rule of exponents.