What is ((6lm^2)/(3l^3m^6))^2 ?

The solution to ((6lm^2)/(3l^3m^6))^2 is 4/(l^4m^8)

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simplify ((6lm^2)/(3l^3m^6))^2

simplify

(\frac{6 l m ^{2}}{3 l ^{3} m ^{6}})^{2}

\frac{4}{l ^{4} m ^{8}}

Solution steps

(\frac{6 l m ^{2}}{3 l ^{3} m ^{6}})^{2}

Apply exponent rule:

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

= \frac{( 6 l m ^{2} ) ^{2}}{( 3 l ^{3} m ^{6} ) ^{2}}

Simplify

(6 l m^{2})^{2} : 36 l^{2} m^{4}

= \frac{36 l ^{2} m ^{4}}{( 3 l ^{3} m ^{6} ) ^{2}}

Simplify

(3 l^{3} m^{6})^{2} : 9 l^{6} m^{12}

= \frac{36 l ^{2} m ^{4}}{9 l ^{6} m ^{12}}

Divide the numbers:

\frac{36}{9} = 4

= \frac{4 l ^{2} m ^{4}}{l ^{6} m ^{12}}

Apply exponent rule:

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

\frac{l ^{2}}{l ^{6}} = \frac{1}{l ^{6 - 2}}

= \frac{4 m ^{4}}{l ^{6 - 2} m ^{12}}

Subtract the numbers:

6 - 2 = 4

= \frac{4 m ^{4}}{l ^{4} m ^{12}}

Apply exponent rule:

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

\frac{m ^{4}}{m ^{12}} = \frac{1}{m ^{12 - 4}}

= \frac{4}{l ^{4} m ^{12 - 4}}

Subtract the numbers:

12 - 4 = 8

= \frac{4}{l ^{4} m ^{8}}

3 x^{- \frac{1}{2}} + 4 x^{\frac{1}{2}} + x^{\frac{3}{2}}

- 3 (x - 4) < 2 (- 2 x - 8) + 12

6 x^{2} + 12 x - 48

x^{2} - 2

- 81 - - 144

What is ((6lm^2)/(3l^3m^6))^2 ?
The solution to ((6lm^2)/(3l^3m^6))^2 is 4/(l^4m^8)