Question
Simplify. Express your answer as the given base raised to a single exponent.
(5 to the power of 17) to the power of 3
(5 to the power of 17) to the power of 3
Answers
GPT-4o mini
To simplify \((5^{17})^3\), we can use the power of a power property of exponents, which states that \((a^m)^n = a^{m \cdot n}\).
Applying this property, we have:
\[
(5^{17})^3 = 5^{17 \cdot 3}
\]
Now calculate \(17 \cdot 3\):
\[
17 \cdot 3 = 51
\]
So, we can rewrite the expression as:
\[
5^{51}
\]
Thus, the simplified form is:
\[
\boxed{5^{51}}
\]
Applying this property, we have:
\[
(5^{17})^3 = 5^{17 \cdot 3}
\]
Now calculate \(17 \cdot 3\):
\[
17 \cdot 3 = 51
\]
So, we can rewrite the expression as:
\[
5^{51}
\]
Thus, the simplified form is:
\[
\boxed{5^{51}}
\]