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Popular >

simplify 3(1/3 ab^2)^3

Solution

simplify

3 (\frac{1}{3} a b^{2})^{3}

Solution

\frac{a ^{3} b ^{6}}{9}

Solution steps

3 (\frac{1}{3} a b^{2})^{3}

Apply exponent rule:

(a \cdot b)^{n} = a^{n} b^{n}

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

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

(\frac{1}{3})^{3} = \frac{1}{27}

= 3 \cdot \frac{1}{27} a^{3} (b^{2})^{3}

Simplify

(b^{2})^{3} : b^{6}

= 3 \cdot \frac{1}{27} a^{3} b^{6}

Simplify

\frac{1}{27} a^{3} b^{6} : \frac{a ^{3} b ^{6}}{27}

= 3 \cdot \frac{a ^{3} b ^{6}}{27}

Apply the fraction rule:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{3 a ^{3} b ^{6}}{27}

Cancel

\frac{3 a ^{3} b ^{6}}{27} : \frac{a ^{3} b ^{6}}{9}

= \frac{a ^{3} b ^{6}}{9}

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Frequently Asked Questions (FAQ)

What is 3(1/3 ab^2)^3 ?
The solution to 3(1/3 ab^2)^3 is (a^3b^6)/9