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Popular >

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

Solution

simplify

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

Solution

\frac{1}{2}

+1

Decimal Notation

0.5

Solution steps

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

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

= \frac{1}{2} \cdot \frac{1}{16} \cdot 4^{2}

4^{2} = 16

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

Factor the number:

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

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

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} \cdot 16

Add the numbers:

1 + 4 = 5

= (\frac{1}{2})^{5} \cdot 16

Apply exponent rule:

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

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

= \frac{1 ^{5}}{2 ^{5}} \cdot 16

1^{5} = 1

= \frac{1}{2 ^{5}} \cdot 16

2^{5} = 32

= \frac{1}{32} \cdot 16

\frac{1}{32} \cdot 16 = \frac{1}{2}

= \frac{1}{2}

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Frequently Asked Questions (FAQ)

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