Asked by woosanâ„
Use the Power Rule of Exponents to simplify the expression (242)5
.(1 point)
Responses
48^5
24^10
24^3
24^7
.(1 point)
Responses
48^5
24^10
24^3
24^7
Answers
Answered by
GPT-4o mini
To simplify the expression \((242)^5\) using the Power Rule of Exponents, we first note that \(242\) can be written as \(2 \times 24\).
However, if we're to consider \(242\) directly, it seems like a misinterpretation because it should be treated as the whole number \(242\) raised to the power of \(5\).
Calculating \( (242)^5 \) directly doesn't seem to align with any of the options given. But if we interpret \(242\) as \(24^2\) (which makes logical sense since none of the other options fit):
So, we simplify it as follows:
\[
(24^2)^5
\]
Using the Power Rule of Exponents, which states that \((a^m)^n = a^{m \cdot n}\):
\[
(24^2)^5 = 24^{2 \cdot 5} = 24^{10}
\]
Thus, the simplified expression is:
\[
24^{10}
\]
So, the correct response is **24^10**.
However, if we're to consider \(242\) directly, it seems like a misinterpretation because it should be treated as the whole number \(242\) raised to the power of \(5\).
Calculating \( (242)^5 \) directly doesn't seem to align with any of the options given. But if we interpret \(242\) as \(24^2\) (which makes logical sense since none of the other options fit):
So, we simplify it as follows:
\[
(24^2)^5
\]
Using the Power Rule of Exponents, which states that \((a^m)^n = a^{m \cdot n}\):
\[
(24^2)^5 = 24^{2 \cdot 5} = 24^{10}
\]
Thus, the simplified expression is:
\[
24^{10}
\]
So, the correct response is **24^10**.