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$7^{(-\frac{1}{2})}$ =

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Evaluate integers raised to positive rational exponents

Full solution

Q.

7^{(-\frac{1}{2})}

=

Understand the exponent: Understand the exponent. $\newline$ The exponent $-\frac{1}{2}$ indicates that we need to find the reciprocal of the square root of $7$ .
Find the square root: Find the square root of $7$ . $\newline$ The square root of $7$ is the number that, when multiplied by itself, gives $7$ . This is not a perfect square, so it cannot be simplified to an integer or simple fraction.
Take the reciprocal: Take the reciprocal of the square root of $7$ . The reciprocal of a number is $1$ divided by that number. So, the reciprocal of the square root of $7$ is $1$ divided by the square root of $7$ .
Write the final answer: Write the final answer. $\newline$ The final answer is the reciprocal of the square root of $7$ , which is written as $\frac{1}{\sqrt{7}}$ or $\sqrt{7}^{-1}$ .

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