Question

which statement is tru out the value of the expression?
$(5^{-1})^2$
it is between -1 and 0.
it is between 0 and 1.
it is less than -1.
it is greater than 1.

Explanation:

Step1: Simplify the exponent

Using the power of a power rule \((a^m)^n = a^{m\times n}\), for \((5^{-1})^2\), we have \(5^{-1\times2}=5^{-2}\).

Step2: Rewrite negative exponent

A negative exponent means the reciprocal, so \(5^{-2}=\frac{1}{5^2}\).

Step3: Calculate the value

\(5^2 = 25\), so \(\frac{1}{5^2}=\frac{1}{25}=0.04\).

Step4: Determine the range

Since \(0 < 0.04 < 1\), the value is between 0 and 1.

Answer:

It is between 0 and 1.