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Answer :
To solve the expression [tex]\(\left(\frac{1}{25}\right)^{-\frac{1}{2}}\)[/tex], we can follow these steps:
1. Understand the Expression:
The expression [tex]\(\left(\frac{1}{25}\right)^{-\frac{1}{2}}\)[/tex] involves a fractional base, [tex]\(\frac{1}{25}\)[/tex], and a negative exponent, [tex]\(-\frac{1}{2}\)[/tex].
2. Simplify the Negative Exponent:
A negative exponent means you take the reciprocal of the base. So, [tex]\((a^{-b}) = \frac{1}{a^{b}}\)[/tex].
Applying this rule, we have:
[tex]\[
\left(\frac{1}{25}\right)^{-\frac{1}{2}} = \left(\frac{25}{1}\right)^{\frac{1}{2}} = 25^{\frac{1}{2}}
\][/tex]
3. Simplify the Fractional Exponent:
An exponent of [tex]\(\frac{1}{2}\)[/tex] means taking the square root of the base. Therefore:
[tex]\[
25^{\frac{1}{2}} = \sqrt{25}
\][/tex]
4. Calculate the Square Root:
The square root of 25 is:
[tex]\[
\sqrt{25} = 5
\][/tex]
Thus, the value of the expression [tex]\(\left(\frac{1}{25}\right)^{-\frac{1}{2}}\)[/tex] is [tex]\(5\)[/tex].
1. Understand the Expression:
The expression [tex]\(\left(\frac{1}{25}\right)^{-\frac{1}{2}}\)[/tex] involves a fractional base, [tex]\(\frac{1}{25}\)[/tex], and a negative exponent, [tex]\(-\frac{1}{2}\)[/tex].
2. Simplify the Negative Exponent:
A negative exponent means you take the reciprocal of the base. So, [tex]\((a^{-b}) = \frac{1}{a^{b}}\)[/tex].
Applying this rule, we have:
[tex]\[
\left(\frac{1}{25}\right)^{-\frac{1}{2}} = \left(\frac{25}{1}\right)^{\frac{1}{2}} = 25^{\frac{1}{2}}
\][/tex]
3. Simplify the Fractional Exponent:
An exponent of [tex]\(\frac{1}{2}\)[/tex] means taking the square root of the base. Therefore:
[tex]\[
25^{\frac{1}{2}} = \sqrt{25}
\][/tex]
4. Calculate the Square Root:
The square root of 25 is:
[tex]\[
\sqrt{25} = 5
\][/tex]
Thus, the value of the expression [tex]\(\left(\frac{1}{25}\right)^{-\frac{1}{2}}\)[/tex] is [tex]\(5\)[/tex].
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