Question

Use the Power Rule of Exponents to create an expression equivalent to (156)2.(1 point)
Responses


15 superscript 12 baseline


15 superscript 4 baseline


15 superscript 3 baseline

15 superscript 8 baseline

Answer 1

To simplify the expression \( (156)^2 \) using the Power Rule of Exponents, we start by breaking down 156 into its prime factors.

The prime factorization of 156 is:
\[ 156 = 4 \times 39 = 4 \times (3 \times 13) = 2^2 \times 3^1 \times 13^1 \]

Now, let's rewrite \( (156)^2 \):

\[
(156)^2 = (2^2 \times 3^1 \times 13^1)^2
\]

Using the Power Rule of Exponents, we apply the exponent of 2 to each factor:

\[
= 2^{2 \times 2} \times 3^{1 \times 2} \times 13^{1 \times 2}
\]
\[
= 2^4 \times 3^2 \times 13^2
\]

Now, instead of exploring the main base of 156, let’s express it as \( 15 \) related for the options given. Since 156 does not break down into 15 easily, we may have a different view on \( 156 \).

Thus, let’s check how it relates back to 15.

So focusing on \( 156 \):
- The only way to express the thought in categorical options you’ve provided:

The answer provided in simplified choices seems likely from unclear relations; based on \( \log_{15} \) of composite of 156. But the expression you may need further breakdown. Likely does seem relevant toward having \( 15^{?} \).


After checking, options need evaluation.

However, the closest answer, in case square on simpler perspective through \( 15^n \),

\[
(15)^1 = 15^1 \text{ – which does not reflect simplified equivalence.}
\]

None of the options you have (based on the factors regrouped into multiples) will hold strictly in \( 15^{?} \) conversion, hence a follow-up needs simple multiplying back through characteristics.

In conclusion: The options seem tied but lack direct simplification or equivalency through factor powers of 15s themselves without additional information.

However, the expressions presented don’t exactly match or portray \( (156)^2 \), which would be considered external unless importance through the framework retrieved.
If retracing becomes clearer toward resolved expectations, please refer back with extended guidance.

If needed for straight rewrite into simplifications that yield equivalence might reconsider or clarify \( 15 ^n \) demonstration versus \( 156^2 \) distinct in feature.

Please guide back through further pathways if it aims toward direct terms \( 15 \) thus.

In conclusion: There isn't a suitable match in right alignment but rather a misinterpretation; choices seem unaligned with \( 156^2 \).