Question

b) how can you write any expression of the form ((a^m)^n) as a single power? ((a^m)^n = )?
options: (a^{m - n}), (a^{m + n}), (a^{mn}), (a^{(m^n)})

Explanation:

Step1: Apply power of a power rule

For $(9^2)^5$, multiply exponents: $2 \times 5 = 10$, so $(9^2)^5 = 9^{10}$.

Step2: Generalize the power rule

For $(a^m)^n$, the power of a power rule states you multiply the exponents, so $(a^m)^n = a^{m \times n} = a^{mn}$.

Answer:

1. $9^{10}$
2. $a^{mn}$