What is (-3a^2*b)^2*(1/(9*a^2*b^3))^4 ?

The solution to (-3a^2*b)^2*(1/(9*a^2*b^3))^4 is 1/(729a^4b^{10)}

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

simplify

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

\frac{1}{729 a ^{4} b ^{10}}

Solution steps

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

Simplify

(- 3 a^{2} b)^{2} : 9 a^{4} b^{2}

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

Simplify

(\frac{1}{9 a ^{2} b ^{3}})^{4} : \frac{1}{6561 a ^{8} b ^{12}}

= 9 a^{4} b^{2} \frac{1}{6561 a ^{8} b ^{12}}

Apply the fraction rule:

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

= \frac{9 a ^{4} b ^{2} \cdot 1}{6561 a ^{8} b ^{12}}

Multiply the numbers:

9 \cdot 1 = 9

= \frac{9 a ^{4} b ^{2}}{6561 a ^{8} b ^{12}}

Factor the number:

6561 = 9 \cdot 729

= \frac{9 a ^{4} b ^{2}}{9 \cdot 729 a ^{8} b ^{12}}

Cancel the common factor:

9

= \frac{a ^{4} b ^{2}}{729 a ^{8} b ^{12}}

Simplify

\frac{a ^{4}}{a ^{8}} : \frac{1}{a ^{4}}

= \frac{b ^{2}}{729 a ^{4} b ^{12}}

Simplify

\frac{b ^{2}}{b ^{12}} : \frac{1}{b ^{10}}

= \frac{1}{729 a ^{4} b ^{10}}

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3 sin (a) - 4 sin^{3} (a)

(5 a + b) 2

What is (-3a^2*b)^2*(1/(9*a^2*b^3))^4 ?
The solution to (-3a^2*b)^2*(1/(9*a^2*b^3))^4 is 1/(729a^4b^{10)}