Question

Find the value of...
(64/25) ^-1/2
Give your answer as fraction in its simplest form

Answer 1

Step-by-step explanation:

${ \frac{64}{25} }^{ \frac{ - 1}{2} }$

${ \frac{64}{25} }^{ \frac{1}{2} }$

${ \frac{64}{25} }^{ \frac{1}{2} } = \sqrt{ \frac{64}{25} } = \frac{8}{5}$

Answer 2

Answer:

$\frac{5}{8}$ is the simplest form $(\frac{64}{25} )^{\frac{-1}{2} }$.

Step-by-step explanation:

Explanation:

• As we know, in general, multiply the powers of a phrase inside a bracket when it has power outside of the bracket. One of the laws of indices is brackets with indices.
• Given in the question, $(\frac{64}{25} )^{\frac{-1}{2} }$
• Step 1:

From the question we have,

$(\frac{64}{25} )^{\frac{-1}{2} }$  and this can be written as,

⇒$(\frac{8^2}{5^2})^{\frac{-1}{2} }$  = $(\frac{8}{5})^{(2){\frac{-1}{2} }}$

[Where $8^2$ = 64 and $5^2$ = 25]

⇒$(\frac{64}{25} )^{\frac{-1}{2} }$ = $(\frac{8}{5})^{-1 }$.

Now, as we know that,

• A fraction with a reversed numerator and denominator is called a reciprocal.

• As a result, negative exponents can be written as the base's positive reciprocal times x.

⇒$\frac{8^{-1}}{5^{-1}}$ = $\frac{5}{8}$.

Final answer:

Hence, the simplest form of $(\frac{64}{25} )^{\frac{-1}{2} }$ is $\frac{5}{8}$.

#SPJ2