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

The solution to ((a^4b^3)/(2a^3b^4*2a^2b^4))^3 is 1/(64a^3b^{15)}

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simplify ((a^4b^3)/(2a^3b^4*2a^2b^4))^3

simplify

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

\frac{1}{64 a ^{3} b ^{15}}

Solution steps

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

Apply exponent rule:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

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

Simplify

(a^{4} b^{3})^{3} : a^{12} b^{9}

= \frac{a ^{12} b ^{9}}{( 2 a ^{3} b ^{4} \cdot 2 a ^{2} b ^{4} ) ^{3}}

Simplify

(2 a^{3} b^{4} \cdot 2 a^{2} b^{4})^{3} : 64 a^{15} b^{24}

= \frac{a ^{12} b ^{9}}{64 a ^{15} b ^{24}}

Apply exponent rule:

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

\frac{a ^{12}}{a ^{15}} = \frac{1}{a ^{15 - 12}}

= \frac{b ^{9}}{64 b ^{24} a ^{15 - 12}}

Subtract the numbers:

15 - 12 = 3

= \frac{b ^{9}}{64 a ^{3} b ^{24}}

Apply exponent rule:

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

\frac{b ^{9}}{b ^{24}} = \frac{1}{b ^{24 - 9}}

= \frac{1}{64 a ^{3} b ^{24 - 9}}

Subtract the numbers:

24 - 9 = 15

= \frac{1}{64 a ^{3} b ^{15}}

- 6 n = - 8

\frac{1}{21} x - \frac{5}{7} = \frac{2}{3}

0.9 (x + 9) = - 0.1 (x - 10)

- 4 x + 5 > - 5

2 x + 6 > 10

What is ((a^4b^3)/(2a^3b^4*2a^2b^4))^3 ?
The solution to ((a^4b^3)/(2a^3b^4*2a^2b^4))^3 is 1/(64a^3b^{15)}