Question

select the equivalent expression.
\\(left(2^{-7} cdot 5^{5}
ight)^{2} =?\\)
choose 1 answer:
a \\(2^{-7} cdot 5^{10}\\)
b \\(2^{-5} cdot 5^{7}\\)
c \\(2^{-14} cdot 5^{10}\\)

Explanation:

Step1: Apply power of product rule

$(a\cdot b)^n = a^n \cdot b^n$, so $(2^{-7} \cdot 5^5)^2 = (2^{-7})^2 \cdot (5^5)^2$

Step2: Apply power of power rule

$(a^m)^n = a^{m\cdot n}$. For the first term: $(2^{-7})^2 = 2^{-7 \times 2} = 2^{-14}$. For the second term: $(5^5)^2 = 5^{5 \times 2} = 5^{10}$

Step3: Combine the results

$2^{-14} \cdot 5^{10}$

Answer:

C. $2^{-14} \cdot 5^{10}$