Question
Use the Power Rule of Exponents to create an expression equivalent to (156)2
.(1 point)
Responses
153
15 cubed
154
15 superscript 4 baseline
1512
15 superscript 12 baseline
158
.(1 point)
Responses
153
15 cubed
154
15 superscript 4 baseline
1512
15 superscript 12 baseline
158
Answers
Answered by
GPT-4o mini
To apply the Power Rule of Exponents, we use the property that \((a^m)^n = a^{m \cdot n}\). In this case, we have:
\[
(156)^2 = (15 \cdot 10 + 6)^2
\]
Now, to simplify:
1. Note that \(156 = 15 \cdot 10 + 6\) is not particularly useful for direct exponentiation.
2. Simply looking at \(156\), one way to approach this is to consider its prime factorization. However, what you need to find is simply an expression equivalent in the way requested.
According to the options provided, let's clarify them related to powers of 15:
1. \(153\) is equivalent to \(15^3\)
2. \(15 \, \text{cubed}\) also represents \(15^3\)
3. \(154\) is equivalent to \(15^4\)
4. \(15^{12}\) indicates a power of \(15\) that is too high.
5. \(158 = 15^8\) involves exponentiation that does not correspond correctly.
Given this confusion, direct multiplication would not provide a route to \(15\).
However, if we were to use the Power Rule fresh on its expression considering the prompt focuses on rewriting:
The expression you would look for can ultimately be factored and examined through dimensional focus:
**Ultimately, given the way you are asking for the connections to powers, you'd have to clarify its placement. But focusing simply from the expressions:**
None of the choices presented simplify to a straightforward route for \(156^2\) at face value or tap a proper \(15\) power directly as desired.
So to give you a resulting equivalency based purely on choices provided through what's laid out would not yield a correct functional form to \(156^2\) thus a need for theoretical or numerical mapping would be essential.
In alignment to proper mathematical adherence - upon checking comprehensive factors or knowing that \(156\) expands but derivatives don't yield clarity, it may be best to derive the numbers via direct application or alternative means.
Sorry for the confusion. Do you want to confirm or clarify a specific approach to parsing?
\[
(156)^2 = (15 \cdot 10 + 6)^2
\]
Now, to simplify:
1. Note that \(156 = 15 \cdot 10 + 6\) is not particularly useful for direct exponentiation.
2. Simply looking at \(156\), one way to approach this is to consider its prime factorization. However, what you need to find is simply an expression equivalent in the way requested.
According to the options provided, let's clarify them related to powers of 15:
1. \(153\) is equivalent to \(15^3\)
2. \(15 \, \text{cubed}\) also represents \(15^3\)
3. \(154\) is equivalent to \(15^4\)
4. \(15^{12}\) indicates a power of \(15\) that is too high.
5. \(158 = 15^8\) involves exponentiation that does not correspond correctly.
Given this confusion, direct multiplication would not provide a route to \(15\).
However, if we were to use the Power Rule fresh on its expression considering the prompt focuses on rewriting:
The expression you would look for can ultimately be factored and examined through dimensional focus:
**Ultimately, given the way you are asking for the connections to powers, you'd have to clarify its placement. But focusing simply from the expressions:**
None of the choices presented simplify to a straightforward route for \(156^2\) at face value or tap a proper \(15\) power directly as desired.
So to give you a resulting equivalency based purely on choices provided through what's laid out would not yield a correct functional form to \(156^2\) thus a need for theoretical or numerical mapping would be essential.
In alignment to proper mathematical adherence - upon checking comprehensive factors or knowing that \(156\) expands but derivatives don't yield clarity, it may be best to derive the numbers via direct application or alternative means.
Sorry for the confusion. Do you want to confirm or clarify a specific approach to parsing?
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