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Popular >

simplify (sqrt(1/3))^4

Solution

simplify

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

Solution

\frac{1}{9}

+1

Decimal Notation

0.11111 \dots

Solution steps

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

Rewrite

4

as

2 \cdot 2

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

Apply exponent rule:

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

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

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

Apply exponent rule:

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

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

Apply exponent rule:

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

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

1^{2} = 1

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

3^{2} = 9

= \frac{1}{9}

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Frequently Asked Questions (FAQ)

What is (sqrt(1/3))^4 ?
The solution to (sqrt(1/3))^4 is 1/9