Use the Power Rule of Exponents to create an expression equivalent to (156)2 .(1 point) Responses 154 15 superscript 4 baseline 153 15 cubed 1512 15 superscript 12 baseline 158

Answer 1

To use the Power Rule of Exponents, we apply the rule that states \(a^m \cdot a^n = a^{m+n}\).

In your expression \((156)^2\), we see that it can be broken down as follows:

\[ (15^1 \cdot 6^1)^2 = 15^{2 \cdot 1} \cdot 6^{2 \cdot 1} = 15^2 \cdot 6^2 \]

This expression does not seem to follow the options directly provided, but if we interpret that we are only needing to express \(156\) in terms of \(15\) without breaking it down into different bases or components, we notice that \(156\) alone to the power of \(2\) indicates that the immediate answer could be questioning the simplification of the statement itself rather than entirely breaking it down as provided.

It appears that none of the provided options such as \(154\), \(15^4\), \(15^3\), \(15^{12}\), or \(15^8\) is directly equivalent to \((156)^2\) in power; however, if looking strictly for a result based on possible corrections or reductions leading to similar structures on impact, \(15^8\) has no relation.

The clarified direct interpretation would lead to:

\((156)^2\) could mathematically revisit to \(15 * 6)^2\); hence, leading to some confusion in association joints of the base.

Clarifying more on this, the more correct direct exponent would yield:

\[ \text{Therefore, if we take expression as is } (156)^2 = 156 \times 156 \]

To answer based thoroughly, more options and contextual scenarios could derive clearly derivative factors:

• Looking back, if intended rectified workings kept toward masses, correcting could yield simpler forms.

Ultimately, since specific numerical equivalents were provided directly needing to clarify divergent paths, revisiting exact phrased numbers in terms always will matter aside derivative multiplicands forming to equate. Please let me know if further specifics on choices or transformations are needed!

Answer 2

Use the Power Rule of Exponents to create an expression equivalent to (156)2 .(1 point) Responses 154 15 superscript 4 baseline 153 15 cubed 1512 15 superscript 12 baseline 158 witch one

Answer 3

To determine which of the options given is equivalent to \((156)^2\) using the Power Rule of Exponents, we'll simplify and analyze it.

1. Break down \(156\): \[ 156 = 15 \cdot 10 + 6 = 15 \cdot 10 + 6 \] However, we can express \(156\) in terms of its base capitals for simplifications. This can divide into relevant integers around key components rather than a strong unit of breakdown; thus keep rooted as is fundamentally in root transfer.

2. Apply the Power Rule: \[ (156)^2 \text{ is already established as a squared base}. \] Now considering potential mappings, analyze potential number-based expression to relate closely to predefined expression responses.

3. Options Analysis:

   • \(154\) doesn't relate.
   • \(15^4\) = ((15^2)^2 \Rightarrow unrelated principles.
   • \(15^3\) = \(15 \cdot 15 \cdot 15\), no direct.
   • \(15^{12}\) = ( (15^4)^3 \Rightarrow significantly higher.
   • \(15^8\) = Relative summation from adjusting would have indicated numerical proportions backtracked as forms.

None of these simplify \((156)^2\) transformatively to fit or resemble normally.

Thus**, closely considered** considering the options:

Closest response is rather outlined through \(15^8\) numerically derivatively from expanses under projections.

But ultimately, since conclusion indicates little direct function other than ( (15)(6) , forward, looking back typically \starting purely:

Unless stated base queries, return could sit within the foundational similarity among relative outputs spread without assorted divergence on recognition as to \(15^8\) on transitions in responses.

Final conclusion—consider finding outputs, guidance might entertain ( (15)(6) \Rightarrow strong contained within directly confirming order in exponent sequences** as needed or articulate it as ( answer at 15^8 conveys ideal along with multipoint checks.

Thus, confirm option as forms aligned based on prior breakdown near \(closing by 15^8\).