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Popular >

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

Solution

simplify

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

Solution

- \frac{1}{8}

+1

Decimal Notation

- 0.125

Solution steps

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

Apply exponent rule:

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

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

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

2^{2} = 4

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

Factor the number:

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

Add the numbers:

1 + 2 = 3

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

Apply exponent rule:

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

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

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

1^{3} = 1

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

2^{3} = 8

= - \frac{1}{8}

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Frequently Asked Questions (FAQ)

What is simplify-1/2 (2)^{-2} ?
The solution to simplify-1/2 (2)^{-2} is -1/8