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)
1 answer
To simplify \(((1/2)^{10})^2\) using the Power Rule of Exponents, we apply the rule which states that \((a^m)^n = a^{m \cdot n}\).
In this case:
\[ ((1/2)^{10})^2 = (1/2)^{10 \cdot 2} = (1/2)^{20}. \]
So, the correct equivalent form from the choices can be represented as:
\[ (1/2)^{(10 \cdot 2)}. \]
Thus, the correct response would be:
\((1/2)^{(10 \times 2)}\).
