Question

Use the power rules for exponents to simplify the expression. Give your answer in exponential form.
(x^4)^3(x^5)^2

Answer 1

To simplify the expression \((x^4)^3 (x^5)^2\), we can use the power rules for exponents, specifically:

1. \((a^m)^n = a^{m \cdot n}\)
2. \(a^m \cdot a^n = a^{m+n}\)

Now let's apply these rules step-by-step:

1. First, simplify \((x^4)^3\):
\[
(x^4)^3 = x^{4 \cdot 3} = x^{12}
\]

2. Next, simplify \((x^5)^2\):
\[
(x^5)^2 = x^{5 \cdot 2} = x^{10}
\]

3. Now, combine the two results using the product rule:
\[
x^{12} \cdot x^{10} = x^{12 + 10} = x^{22}
\]

Therefore, the simplified expression in exponential form is:
\[
\boxed{x^{22}}
\]