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Popular >

simplify (9^{-3}*16^{3/2})^{1/6}

Solution

simplify

(9^{- 3} \cdot 1 6^{\frac{3}{2}})^{\frac{1}{6}}

Solution

\frac{2}{3}

+1

Solution steps

(9^{- 3} \cdot 1 6^{\frac{3}{2}})^{\frac{1}{6}}

Apply exponent rule:

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

(9^{- 3} \cdot 1 6^{\frac{3}{2}})^{\frac{1}{6}} = (9^{- 3})^{\frac{1}{6}} (1 6^{\frac{3}{2}})^{\frac{1}{6}}

= (9^{- 3})^{\frac{1}{6}} (1 6^{\frac{3}{2}})^{\frac{1}{6}}

(9^{- 3})^{\frac{1}{6}} = \frac{1}{3}

= \frac{1}{3} (1 6^{\frac{3}{2}})^{\frac{1}{6}}

Apply exponent rule:

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

(1 6^{\frac{3}{2}})^{\frac{1}{6}} = 1 6^{\frac{3}{2} \cdot \frac{1}{6}}

= \frac{1}{3} \cdot 1 6^{\frac{3}{2} \cdot \frac{1}{6}}

\frac{3}{2} \cdot \frac{1}{6} = \frac{1}{4}

= \frac{1}{3} \cdot 1 6^{\frac{1}{4}}

Factor the number:

16 = 2^{4}

= \frac{1}{3} (2^{4})^{\frac{1}{4}}

Apply exponent rule:

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

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

= \frac{1}{3} \cdot 2^{4 \cdot \frac{1}{4}}

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

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

Apply exponent rule:

a^{1} = a

2^{1} = 2

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

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

= \frac{2}{3}

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Frequently Asked Questions (FAQ)

What is (9^{-3}*16^{3/2})^{1/6} ?
The solution to (9^{-3}*16^{3/2})^{1/6} is 2/3