What is (2b^{-3})^2 ?

The solution to (2b^{-3})^2 is 4/(b^6)

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simplify (2b^{-3})^2

simplify

(2 b^{- 3})^{2}

\frac{4}{b ^{6}}

Solution steps

(2 b^{- 3})^{2}

Apply exponent rule:

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

(2 b^{- 3})^{2} = 2^{2} (b^{- 3})^{2}

= 2^{2} (b^{- 3})^{2}

2^{2} = 4

= 4 (b^{- 3})^{2}

Apply exponent rule:

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

assuming

a \geq 0

(b^{- 3})^{2} = b^{- 3 \cdot 2}

= 4 b^{- 3 \cdot 2}

Multiply the numbers:

3 \cdot 2 = 6

= 4 b^{- 6}

Apply exponent rule:

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

b^{- 6} = \frac{1}{b ^{6}}

= 4 \cdot \frac{1}{b ^{6}}

Simplify

4 \cdot \frac{1}{b ^{6}} : \frac{4}{b ^{6}}

= \frac{4}{b ^{6}}

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