Use the Power Rule of Exponents to simplify the expression (242)5

.(1 point)
Responses

48^5

24^10

24^3

24^7

1 answer

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.