What is ((2^m)/(2^{-3)})^2 ?

The solution to ((2^m)/(2^{-3)})^2 is 2^{2m+6}

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simplify ((2^m)/(2^{-3)})^2

simplify

(\frac{2 ^{m}}{2 ^{- 3}})^{2}

2^{2 m + 6}

Solution steps

(\frac{2 ^{m}}{2 ^{- 3}})^{2}

Apply exponent rule:

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

= \frac{( 2 ^{m} ) ^{2}}{( 2 ^{- 3} ) ^{2}}

Simplify

(2^{m})^{2} : 4^{m}

= \frac{4 ^{m}}{( 2 ^{- 3} ) ^{2}}

(2^{- 3})^{2} = \frac{1}{64}

= \frac{4 ^{m}}{\frac{1}{64}}

Apply the fraction rule:

\frac{a}{\frac{b}{c}} = \frac{a \cdot c}{b}

= \frac{4 ^{m} \cdot 64}{1}

Apply rule

\frac{a}{1} = a

= 64 \cdot 4^{m}

Factor integer

4 = 2^{2}

= (2^{2})^{m} \cdot 64

Apply exponent rule:

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

(2^{2})^{m} = 2^{2 m}

= 2^{2 m} \cdot 64

Factor integer

64 = 2^{6}

= 2^{2 m} \cdot 2^{6}

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

2^{2 m} \cdot 2^{6} = 2^{2 m + 6}

= 2^{2 m + 6}

sec (θ) cos (θ)

(1 - cos (2 x))^{2}

sin^{4} (θ) - cos^{4} (θ)

x^{2} + 15 x + 14

\frac{1 0 ^{3} \cdot 10 0 ^{2} \cdot 100 0 ^{4}}{( 1 0 ^{2} ) ^{5} \cdot 100}