Question

Which expression is equivalent to (53)-2?

Answer 1

2(-53)

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Answer 2

Answer:

The expression $\frac{1}{5\times 5\times 5\times 5\times 5\times 5}$ is equivalent to the given expression.

Step-by-step explanation:

The given expression is

$(5^3)^{-2}$

We need to find the expression which is equivalent to the given expression.

Using power to power property of exponent, we get

$(5^3)^{-2}=5^{3\times (-2)}$          $[\because (a^m)^n=a^{mn}]$

$(5^3)^{-2}=5^{-6}$

Using quotient property of exponents, we get

$(5^3)^{-2}=\frac{1}{5^{6}}$          $[\because a^{-n}=\frac{1}{a^n}]$

$(5^3)^{-2}=\frac{1}{5\times 5\times 5\times 5\times 5\times 5}$

Therefore the expression $\frac{1}{5\times 5\times 5\times 5\times 5\times 5}$ is equivalent to the given expression.