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Popular >

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

Solution

simplify

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

Solution

\frac{9}{2}

+1

Decimal Notation

4.5

Solution steps

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

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

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

Apply exponent rule:

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

6^{- 1} = \frac{1}{6}

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

Factor the number:

9 = 3^{2}

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

Apply exponent rule:

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

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

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

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

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

3^{3} = 27

= \frac{1}{6} \cdot 27

\frac{1}{6} \cdot 27 = \frac{9}{2}

= \frac{9}{2}

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Frequently Asked Questions (FAQ)

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