simplify (2^{-6})^2

Solution

simplify

(2^{- 6})^{2}

\frac{1}{4096}

Solution steps

(2^{- 6})^{2}

Apply exponent rule:

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

= 2^{- 6 \cdot 2}

Multiply the numbers:

6 \cdot 2 = 12

= 2^{- 12}

Apply exponent rule:

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

2^{- 12} = \frac{1}{2 ^{12}}

= \frac{1}{2 ^{12}}

2^{12} = 4096

= \frac{1}{4096}

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