What is (27m)^{2/3}(4m)^{1/2} ?

The solution to (27m)^{2/3}(4m)^{1/2} is 18m^{7/6}

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simplify (27m)^{2/3}(4m)^{1/2}

simplify

(27 m)^{\frac{2}{3}} (4 m)^{\frac{1}{2}}

18 m^{\frac{7}{6}}

Solution steps

(27 m)^{\frac{2}{3}} (4 m)^{\frac{1}{2}}

Simplify

(27 m)^{\frac{2}{3}} : 9 m^{\frac{2}{3}}

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

Simplify

(4 m)^{\frac{1}{2}} : 2 m^{\frac{1}{2}}

= 9 m^{\frac{2}{3}} \cdot 2 m^{\frac{1}{2}}

Multiply the numbers:

9 \cdot 2 = 18

= 18 m^{\frac{2}{3}} m^{\frac{1}{2}}

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

m^{\frac{2}{3}} m^{\frac{1}{2}} = m^{\frac{2}{3} + \frac{1}{2}}

= 18 m^{\frac{2}{3} + \frac{1}{2}}

\frac{2}{3} + \frac{1}{2} = \frac{7}{6}

= 18 m^{\frac{7}{6}}

5 x^{3} - 10 x + 5 x

8 x^{2} + 14 x - 15

5 x^{2} - x - 4 = 0

50 + \frac{N - 40}{4} 5 0^{o} f

z^{2} - 9

What is (27m)^{2/3}(4m)^{1/2} ?
The solution to (27m)^{2/3}(4m)^{1/2} is 18m^{7/6}