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

The solution to ((2a^{-1})^2)/((2a^{-1))^{-2}} is (16)/(a^4)

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

simplify

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

\frac{16}{a ^{4}}

Solution steps

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

Apply exponent rule:

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

= (2 a^{- 1})^{2 - (- 2)}

Apply rule

- (- a) = a

= (2 a^{- 1})^{2 + 2}

Multiply

2 a^{- 1} : \frac{2}{a}

= (\frac{2}{a})^{2 + 2}

Add the numbers:

2 + 2 = 4

= (\frac{2}{a})^{4}

Apply exponent rule:

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

= \frac{2 ^{4}}{a ^{4}}

2^{4} = 16

= \frac{16}{a ^{4}}

61

2 x - 3 = 15

2 x^{2} + x + 2 = 0

3 x^{2} + x = 4

\frac{30 ab}{35 b c}

What is ((2a^{-1})^2)/((2a^{-1))^{-2}} ?
The solution to ((2a^{-1})^2)/((2a^{-1))^{-2}} is (16)/(a^4)