What is (-3a^{1/4})(9a)^{-3/2} ?

The solution to (-3a^{1/4})(9a)^{-3/2} is -1/(9a^{5/4)}

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simplify (-3a^{1/4})(9a)^{-3/2}

simplify

(- 3 a^{\frac{1}{4}}) (9 a)^{- \frac{3}{2}}

- \frac{1}{9 a ^{\frac{5}{4}}}

Solution steps

(- 3 a^{\frac{1}{4}}) (9 a)^{- \frac{3}{2}}

Apply rule:

(- a) = - a

(- 3 a^{\frac{1}{4}}) = - 3 a^{\frac{1}{4}}

= - 3 a^{\frac{1}{4}} (9 a)^{- \frac{3}{2}}

Simplify

(9 a)^{- \frac{3}{2}} : \frac{1}{27 a ^{\frac{3}{2}}}

= - 3 a^{\frac{1}{4}} \frac{1}{27 a ^{\frac{3}{2}}}

Apply the fraction rule:

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

= - \frac{3 a ^{\frac{1}{4}} \cdot 1}{27 a ^{\frac{3}{2}}}

Multiply the numbers:

3 \cdot 1 = 3

= - \frac{3 a ^{\frac{1}{4}}}{27 a ^{\frac{3}{2}}}

Factor the number:

27 = 3 \cdot 9

= - \frac{3 a ^{\frac{1}{4}}}{3 \cdot 9 a ^{\frac{3}{2}}}

Cancel the common factor:

3

= - \frac{a ^{\frac{1}{4}}}{9 a ^{\frac{3}{2}}}

Simplify

\frac{a ^{\frac{1}{4}}}{a ^{\frac{3}{2}}} : \frac{1}{a ^{\frac{5}{4}}}

= - \frac{1}{9 a ^{\frac{5}{4}}}

8 x \leq 56

8 n^{4} - 2 n^{2} - 1

2 x + 7 < - 3 x + 12

x^{2} - x + 16 = 0

7 \cdot 7 \cdot 7 \cdot 7 \cdot 7 \cdot 7

What is (-3a^{1/4})(9a)^{-3/2} ?
The solution to (-3a^{1/4})(9a)^{-3/2} is -1/(9a^{5/4)}