Question

Simplify: [(625)-1/4]^2
​

Answer 1

Answer:

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Step-by-step explanation:

By simplifying the given equation we get the answer as 5.

Step-by-step explanation:

To simplify: [\{(625)^{-\frac{1}{2}}\}^{\frac{1}{4}}]^{2}[{(625)

−

2

1

}

4

1

]

2

, powers have to be multiplied

Consider the powers [\frac{-1}{2} \times \frac{-1}{4}]^{2}=[\frac{-1}{2} \times \frac{-1}{4}] \times 2[

2

−1

×

4

−1

]

2

=[

2

−1

×

4

−1

]×2

\begin{gathered}\begin{array}{l}{=[\frac{-1}{2} \times \frac{-1}{2}]=\frac{1}{4}} \\ {(625)^{\frac{1}{4}}=(5 \times 5 \times 5 \times 5)^{\frac{1}{4}}} \\ {=(5)^{4}(\frac{1}{4})}\end{array}\end{gathered}

=[

2

−1

×

2

−1

]=

4

1

(625)

4

1

=(5×5×5×5)

4

1

=(5)

4

(

4

1

)

Therefore, [\{(625)^{-\frac{1}{2}}\}^{\frac{1}{4}}]^{2}[{(625)

−

2

1

}

4

1

]

2

= 5

Answer 2

Step-by-step explanation:

by simplification

$( {625 - \frac{1}{4} })^{2}$

clearly 625 = 25² and 4 = 2²

then

$( { {25}^{2} - { \frac{1}{2} }^{2} ) }^{2}$

in side of barcket we can see property of a²- b²

so

$({25 + \frac{1}{2})(25 - \frac{1}{2} )}^{2}$

then

$( { \frac{50 + 1}{2})( \frac{50 - 1}{2} )}^{2}$

$( { \frac{51}{2})( \frac{49}{2}) }^{2}$

${ \frac{2499}{4} }^{2}$

${624.75}^{2}$

$390,312.5625$

here is your answer mate

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