Which of the following correctly used the Power Rule of Exponents in the expression (10 to the ninth power) to the seventh power.

Question

1. 10 to the sixty third power?
2. 10 to the second power?
3. 10 to the sixteenth power?
4. 90 to the seventh power?

Answer 1

The Power Rule of Exponents states that when raising a power to another power, you multiply the exponents. In the expression \( (10^9)^7 \), you would apply the Power Rule as follows:

\[ (10^9)^7 = 10^{9 \times 7} = 10^{63} \]

Based on this, the correct choice that uses the Power Rule of Exponents correctly is:

1. \( 10^{63} \)

So, the answer is option 1: \( 10 \) to the sixty third power.