What is ((3ab)^3)/(2ab^2(6a)^2) ?

The solution to ((3ab)^3)/(2ab^2(6a)^2) is (3b)/8

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simplify ((3ab)^3)/(2ab^2(6a)^2)

simplify

\frac{( 3 ab ) ^{3}}{2 a b ^{2} ( 6 a ) ^{2}}

\frac{3 b}{8}

Solution steps

\frac{( 3 ab ) ^{3}}{2 a b ^{2} ( 6 a ) ^{2}}

Apply exponent rule:

(a \cdot b)^{n} = a^{n} b^{n}

(3 ab)^{3} = 3^{3} a^{3} b^{3}

= \frac{3 ^{3} a ^{3} b ^{3}}{2 a b ^{2} ( 6 a ) ^{2}}

Apply exponent rule:

(a \cdot b)^{n} = a^{n} b^{n}

(6 a)^{2} = 6^{2} a^{2}

= \frac{3 ^{3} a ^{3} b ^{3}}{2 a b ^{2} \cdot 6 ^{2} a ^{2}}

Factor

6^{2} : 3^{2} \cdot 2^{2}

= \frac{3 ^{3} a ^{3} b ^{3}}{2 a b ^{2} \cdot 3 ^{2} \cdot 2 ^{2} a ^{2}}

\frac{3 ^{3}}{3 ^{2}} = 3

= \frac{3 a ^{3} b ^{3}}{2 a b ^{2} \cdot 2 ^{2} a ^{2}}

Simplify

\frac{a ^{3}}{a} : a^{2}

= \frac{3 a ^{2} b ^{3}}{2 b ^{2} \cdot 2 ^{2} a ^{2}}

Cancel the common factor:

a^{2}

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

Simplify

\frac{b ^{3}}{b ^{2}} : b

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

Simplify

\frac{3 b}{2 \cdot 2 ^{2}} : \frac{3 b}{8}

= \frac{3 b}{8}

\frac{1}{5} (3 x + 2) - \frac{1}{3} (x + 4) = 6

4 (x - 5)^{2} + 8 (x - 5)

x^{2} + 2 x - 10 = 0

4 h < 8

What is ((3ab)^3)/(2ab^2(6a)^2) ?
The solution to ((3ab)^3)/(2ab^2(6a)^2) is (3b)/8