# Determine: (2b^4)^(-1)

Determine: $\left(2{b}^{4}{\right)}^{-1}$
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Step 1
The rule for raising a power to a power is that you multiply the exponents. Combining that with the Distributive Property yeilds the following:
$\left(A{B}^{M}{\right)}^{N}={A}^{N}{B}^{MN}$
In this case,
Also, the rule for negative expontents is that they go in the denominator as follows:
${A}^{-M}=\frac{1}{{A}^{M}}$
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Leypoldon
Step 1
$\left(1{b}^{4}{\right)}^{-1}={2}^{-1}×{b}^{4×-1}\phantom{\rule{0ex}{0ex}}=\frac{1}{2}×\frac{1}{{b}^{4}}\phantom{\rule{0ex}{0ex}}=\frac{1}{2×{b}^{4}}$