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Popular >

simplify 1/2*4^{-2}

Solution

simplify

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

Solution

\frac{1}{32}

+1

Solution steps

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

Apply exponent rule:

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

4^{- 2} = \frac{1}{4 ^{2}}

= \frac{1}{2} \cdot \frac{1}{4 ^{2}}

4^{2} = 16

= \frac{1}{2} \cdot \frac{1}{16}

Factor the number:

\frac{1}{16} = (\frac{1}{2})^{4}

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

Apply exponent rule:

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

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

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

Add the numbers:

1 + 4 = 5

= (\frac{1}{2})^{5}

Apply exponent rule:

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

= \frac{1 ^{5}}{2 ^{5}}

1^{5} = 1

= \frac{1}{2 ^{5}}

2^{5} = 32

= \frac{1}{32}

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Frequently Asked Questions (FAQ)

What is 1/2*4^{-2} ?
The solution to 1/2*4^{-2} is 1/32