What is ((12a^3b^5)/(4a^6b^3))^3 ?

The solution to ((12a^3b^5)/(4a^6b^3))^3 is (27b^6)/(a^9)

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simplify ((12a^3b^5)/(4a^6b^3))^3

simplify

(\frac{12 a ^{3} b ^{5}}{4 a ^{6} b ^{3}})^{3}

\frac{27 b ^{6}}{a ^{9}}

Solution steps

(\frac{12 a ^{3} b ^{5}}{4 a ^{6} b ^{3}})^{3}

Apply exponent rule:

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

= \frac{( 12 a ^{3} b ^{5} ) ^{3}}{( 4 a ^{6} b ^{3} ) ^{3}}

Simplify

(12 a^{3} b^{5})^{3} : 1728 a^{9} b^{15}

= \frac{1728 a ^{9} b ^{15}}{( 4 a ^{6} b ^{3} ) ^{3}}

Simplify

(4 a^{6} b^{3})^{3} : 64 a^{18} b^{9}

= \frac{1728 a ^{9} b ^{15}}{64 a ^{18} b ^{9}}

Divide the numbers:

\frac{1728}{64} = 27

= \frac{27 a ^{9} b ^{15}}{a ^{18} b ^{9}}

Apply exponent rule:

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

\frac{a ^{9}}{a ^{18}} = \frac{1}{a ^{18 - 9}}

= \frac{27 b ^{15}}{b ^{9} a ^{18 - 9}}

Subtract the numbers:

18 - 9 = 9

= \frac{27 b ^{15}}{a ^{9} b ^{9}}

Apply exponent rule:

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

\frac{b ^{15}}{b ^{9}} = b^{15 - 9}

= \frac{27 b ^{15 - 9}}{a ^{9}}

Subtract the numbers:

15 - 9 = 6

= \frac{27 b ^{6}}{a ^{9}}

18 < 4 x + 2 < 24

y^{17}

9 v - 30 = 5 v - 6

2 < x - 3 < 2 x

4 x^{2} - 7 x < - 3

What is ((12a^3b^5)/(4a^6b^3))^3 ?
The solution to ((12a^3b^5)/(4a^6b^3))^3 is (27b^6)/(a^9)