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Select the equivalent expression.

(2^(-7)*5^(5))^(2)=?
Choose 1 answer:
(A)
2^(-14)*5^(10)
(B)
2^(-5)*5^(7)
(C)
2^(-7)*5^(10)

Select the equivalent expression. $\newline$ $(2^{-7}\cdot5^{5})^{2}=$ ? $\newline$ Choose $1$ answer: $\newline$ (A) $2^{-14}\cdot5^{10}$ $\newline$ (B) $2^{-5}\cdot5^{7}$ $\newline$ (C) $2^{-7}\cdot5^{10}$

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Evaluate expressions using properties of exponents

Full solution

Q. Select the equivalent expression.

\newline

(2^{-7}\cdot5^{5})^{2}=

?

\newline

Choose

1

answer:

\newline

(A)

2^{-14}\cdot5^{10}

\newline

(B)

2^{-5}\cdot5^{7}

\newline

(C)

2^{-7}\cdot5^{10}

Identify properties of exponents: Identify the properties of exponents to be used. When raising a power to a power, you multiply the exponents $(a^{m})^{n} = a^{m \times n}$ .
Apply power of a product rule: Apply the power of a product rule: $(a*b)^n = a^n * b^n$ . Here, $a = 2^{-7}$ , $b = 5^{5}$ , and $n = 2$ .
Calculate new exponents: Calculate the new exponents by multiplying: $(2^{-7})^2 = 2^{-14}$ and $(5^{5})^2 = 5^{10}$ .
Combine results: Combine the results to get the final expression: $2^{-14} \times 5^{10}$ .
Choose equivalent expression: Choose the equivalent expression from the given options. The correct answer is (A) $2^{-14}\cdot 5^{10}$ .

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