Question

Using the Power Rule of Exponents, what is an equivalent form of ((12)10)2 ?(1 point)Responses(12)(10−2)left parenthesis Start Fraction 1 over 2 End Fraction right parenthesis superscript left parenthesis 10 minus 2 right parenthesis baseline(12)(10⋅2)left parenthesis Start Fraction 1 over 2 End Fraction right parenthesis superscript left parenthesis 10 times 2 right parenthesis baseline(12)(10÷2)left parenthesis Start Fraction 1 over 2 End Fraction right parenthesis superscript left parenthesis 10 divided by 2 right parenthesis baseline(12)(10+2)

Answer 1

To simplify \(((12)^{10})^2\) using the Power Rule of Exponents, you multiply the exponents. The Power Rule states that \((a^m)^n = a^{m \cdot n}\).

Applying this rule:

\[ ((12)^{10})^2 = 12^{10 \cdot 2} = 12^{20} \]

Now let's look at the options provided:

1. \((12)(10^{-2})\)
2. \((12)(10 \cdot 2)\)
3. \((12)(10 \div 2)\)
4. \((12)(10 + 2)\)

None of these options directly reflect the simplified result \(12^{20}\). Thus, it appears that there may be an issue with the options provided, or additional context may be required to determine an equivalent expression within the provided choices.

If re-evaluating the problem specifically for the options given (if they are framing the expression differently or tweaking it), it's still essential to focus on the result via the Power Rule as initially described.

The simplest equivalent form from just the exponents is related to just \(12^{20}\), which doesn't resonate with any options provided.

Make sure to verify if there is any confusion, or ask for other potential equivalents or representation meant to be approximated through these choices.

Considering the strict evaluation, do let me know if further clarification is needed.

Answer 2

when did I say to simplify it?

Answer 3

I apologize for misunderstanding your request. You asked for an equivalent form using the Power Rule of Exponents. Given the expression \(((12)^{10})^2\), we can indeed express it using the Power Rule, but without simplifying to a single exponent.

The Power Rule states that \((a^m)^n = a^{m \cdot n}\). Thus:

\[ ((12)^{10})^2 = (12)^{10 \cdot 2} = (12)^{20} \]

However, in terms of how the question presents options, none of those match directly with the operation of exponents.

The correct interpretation of using the Power Rule while considering various forms might suggest generating equivalent through combination formats regarding the inputs, yet the options given are more algebraic manipulations.

If we revisit the multiplication format as in a product, rather than simplifying:

None of the provided responses are true applications of exponent rules or depict an accurate transformation of the expression \(((12)^{10})^2\) in light of direct numeric/product transformations.

If clarification is needed, please provide further details or specify what type of equivalent form you seek! Thank you for your patience!