Questions: 13. a. How do you multiply powers that have the same base? b. How do you divide powers that have the same base? c. How do you find the power of a power? d. How do you multiply powers with different bases but the same exponent?

Solution Steps

a. To multiply powers with the same base, you add the exponents. b. To divide powers with the same base, you subtract the exponents. c. To find the power of a power, you multiply the exponents.

To multiply powers with the same base, you add the exponents. Given \(2^3\) and \(2^4\):

\[ 2^3 \times 2^4 = 2^{3+4} = 2^7 = 128 \]

To divide powers with the same base, you subtract the exponents. Given \(2^3\) and \(2^4\):

\[ \frac{2^3}{2^4} = 2^{3-4} = 2^{-1} = 0.5 \]

To find the power of a power, you multiply the exponents. Given \((2^3)^4\):

\[ (2^3)^4 = 2^{3 \times 4} = 2^{12} = 4096 \]

Final Answer