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Popular >

simplify (5a^{-2})^2

Solution

simplify

(5 a^{- 2})^{2}

Solution

\frac{25}{a ^{4}}

Solution steps

(5 a^{- 2})^{2}

Apply exponent rule:

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

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

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

5^{2} = 25

= 25 (a^{- 2})^{2}

Apply exponent rule:

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

assuming

a \geq 0

(a^{- 2})^{2} = a^{- 2 \cdot 2}

= 25 a^{- 2 \cdot 2}

Multiply the numbers:

2 \cdot 2 = 4

= 25 a^{- 4}

Apply exponent rule:

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

a^{- 4} = \frac{1}{a ^{4}}

= 25 \cdot \frac{1}{a ^{4}}

Simplify

25 \cdot \frac{1}{a ^{4}} : \frac{25}{a ^{4}}

= \frac{25}{a ^{4}}

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Frequently Asked Questions (FAQ)

What is (5a^{-2})^2 ?
The solution to (5a^{-2})^2 is (25)/(a^4)