Question

Select the equivalent expression. \[\left(2^{-7}\cdot 5^{5}\right)^{2}=?\] choose 1 answer: choose 1 answer: (choice a) \[2^{-5}\cdot 5^{7}\] a \[2^{-5}\cdot 5^{7}\] (choice b) \[2^{-7}\cdot 5^{10}\] b \[2^{-7}\cdot 5^{10}\] (choice c) \[2^{-14}\cdot 5^{10}\] c \[2^{-14}\cdot 5^{10}\]

Answer 1

The equivalent expression is
`\[2^(-14)\cdot 5^(10)\].`

Thus the correct option is (C).

Step-by-step explanation:

To simplify the given expression
`\[\left(2^(-7)\cdot 5^(5)\right)^(2)\],` apply the exponentiation rule, which states that when an exponent is raised to another exponent, you multiply the exponents. In this case,
`\(2^(-7)\)` is squared to give
`\(2^(-14)\),` and
`\(5^(5)\)`is squared to give
`\(5^(10)\)`.

Therefore,
`\[\left(2^(-7)\cdot 5^(5)\right)^(2) = 2^(-14)\cdot 5^(10)\]`.

Comparing this with the choices provided, the correct equivalent expression is found in choice c:
`\[2^(-14)\cdot 5^(10)\]`. This is because it correctly represents the squared form of the given expression, satisfying the exponentiation rule. Thus, choice c is the accurate and equivalent expression for
`\[\left(2^(-7)\cdot 5^(5)\right)^(2)\].`

Thus the correct option is (C).