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Popular >

simplify (5*5^{-4})^2

Solution

simplify

(5 \cdot 5^{- 4})^{2}

Solution

\frac{1}{15625}

+1

Decimal Notation

0.000064

Solution steps

(5 \cdot 5^{- 4})^{2}

Apply exponent rule:

(a \cdot b)^{n} = a^{n} b^{n}

(5 \cdot 5^{- 4})^{2} = 5^{2} (5^{- 4})^{2}

= 5^{2} (5^{- 4})^{2}

5^{2} = 25

= 25 (5^{- 4})^{2}

Apply exponent rule:

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

(5^{- 4})^{2} = 5^{- 4 \cdot 2}

= 25 \cdot 5^{- 4 \cdot 2}

Multiply the numbers:

4 \cdot 2 = 8

= 25 \cdot 5^{- 8}

Apply exponent rule:

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

5^{- 8} = \frac{1}{5 ^{8}}

= 25 \cdot \frac{1}{5 ^{8}}

5^{8} = 390625

= 25 \cdot \frac{1}{390625}

25 \cdot \frac{1}{390625} = \frac{1}{15625}

= \frac{1}{15625}

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Frequently Asked Questions (FAQ)

What is (5*5^{-4})^2 ?
The solution to (5*5^{-4})^2 is 1/15625