What is (1/4)(5^{-2})^{4.625} ?

The solution to (1/4)(5^{-2})^{4.625} is 1/(4*5^{9.25)}

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simplify (1/4)(5^{-2})^{4.625}

simplify

(\frac{1}{4}) (5^{- 2})^{4.625}

\frac{1}{4 \cdot 5 ^{9.25}}

Decimal Notation

8.55988 E - 8

Solution steps

(\frac{1}{4}) (5^{- 2})^{4.625}

Apply rule:

(a) = a

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

= \frac{1}{4} (5^{- 2})^{4.625}

Apply exponent rule:

(a^{b})^{c} = a^{b c}, a \geq 0

(5^{- 2})^{4.625} = 5^{- 2 \cdot 4.625}

= \frac{1}{4} \cdot 5^{- 2 \cdot 4.625}

Multiply the numbers:

2 \cdot 4.625 = 9.25

= \frac{1}{4} \cdot 5^{- 9.25}

Apply exponent rule:

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

5^{- 9.25} = \frac{1}{5 ^{9.25}}

= \frac{1}{4} \cdot \frac{1}{5 ^{9.25}}

\frac{1}{4} \cdot \frac{1}{5 ^{9.25}} = \frac{1}{4 \cdot 5 ^{9.25}}

= \frac{1}{4 \cdot 5 ^{9.25}}

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What is (1/4)(5^{-2})^{4.625} ?
The solution to (1/4)(5^{-2})^{4.625} is 1/(4*5^{9.25)}