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Popular >

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

Solution

simplify

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

Solution

\frac{1}{64}

+1

Decimal Notation

0.015625

Solution steps

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

Apply exponent rule:

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

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

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

4^{2} = 16

= \frac{1}{4} \cdot \frac{1}{16}

Factor the number:

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

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

Apply exponent rule:

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

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

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

Add the numbers:

1 + 2 = 3

= (\frac{1}{4})^{3}

Apply exponent rule:

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

= \frac{1 ^{3}}{4 ^{3}}

1^{3} = 1

= \frac{1}{4 ^{3}}

4^{3} = 64

= \frac{1}{64}

Popular Examples

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\frac{x}{8} - 9 = 1

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Frequently Asked Questions (FAQ)

What is 1/4 (4)^{-2} ?
The solution to 1/4 (4)^{-2} is 1/64