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

The solution to 2^{-x}(x^3)^{-x} is 1/(2^xx^{3x)}

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

simplify

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

\frac{1}{2 ^{x} x ^{3 x}}

Solution steps

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

Apply exponent rule:

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

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

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

Simplify

(x^{3})^{- x} : \frac{1}{x ^{3 x}}

= \frac{1}{2 ^{x}} \cdot \frac{1}{x ^{3 x}}

Apply the fraction rule:

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

= \frac{1 \cdot 1}{2 ^{x} x ^{3 x}}

Multiply the numbers:

1 \cdot 1 = 1

= \frac{1}{2 ^{x} x ^{3 x}}

h (t + 1)

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