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Popular >

simplify 1/2*(1/4)^{-1}

Solution

simplify

\frac{1}{2} \cdot (\frac{1}{4})^{- 1}

Solution

2

Solution steps

\frac{1}{2} (\frac{1}{4})^{- 1}

Factor the number:

\frac{1}{4} = (\frac{1}{2})^{2}

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

Apply exponent rule:

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

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

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

2 (- 1) = - 2

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

Apply exponent rule:

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

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

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

Subtract the numbers:

1 - 2 = - 1

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

Apply exponent rule:

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

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

= \frac{1}{\frac{1}{2}}

\frac{1}{\frac{1}{2}} = 2

= 2

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Frequently Asked Questions (FAQ)

What is 1/2*(1/4)^{-1} ?
The solution to 1/2*(1/4)^{-1} is 2