What is (((1/5)^{-2})^2)^{1/2} ?

The solution to (((1/5)^{-2})^2)^{1/2} is 25

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simplify (((1/5)^{-2})^2)^{1/2}

simplify

((\frac{1}{5})^{- 2})^{2}^{\frac{1}{2}}

25

Solution steps

((\frac{1}{5})^{- 2})^{2}^{\frac{1}{2}}

((\frac{1}{5})^{- 2})^{2} : (\frac{1}{5})^{- 4}

= ((\frac{1}{5})^{- 4})^{\frac{1}{2}}

Apply exponent rule:

(a^{b})^{c} = a^{b c}

= (\frac{1}{5})^{(- 4) \frac{1}{2}}

(- 4) \frac{1}{2} = - 2

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

Apply exponent rule:

a^{- b} = \frac{1}{a ^{b}}

= \frac{1}{( \frac{1}{5} ) ^{2}}

Apply exponent rule:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

(\frac{1}{5})^{2} = \frac{1 ^{2}}{5 ^{2}}

= \frac{1}{\frac{1 ^{2}}{5 ^{2}}}

Apply the fraction rule:

\frac{1}{\frac{b}{c}} = \frac{c}{b}

= \frac{5 ^{2}}{1 ^{2}}

Apply rule

1^{a} = 1

1^{2} = 1

= \frac{5 ^{2}}{1}

Apply the fraction rule:

\frac{a}{1} = a

= 5^{2}

5^{2} = 25

= 25

(2.7 x \cdot 1 0^{4}) (3.5 x \cdot 1 0^{3})

20 e^{- 0.5 (7)}