What is (12/7 x^{3m-(1/3)})^3*(7/12 x^{(1/3)})^3 ?

The solution to (12/7 x^{3m-(1/3)})^3*(7/12 x^{(1/3)})^3 is x^{9m}

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simplify (12/7 x^{3m-(1/3)})^3*(7/12 x^{(1/3)})^3

simplify

(\frac{12}{7} x^{3 m - (\frac{1}{3})})^{3} \cdot (\frac{7}{12} x^{(\frac{1}{3})})^{3}

x^{9 m}

Solution steps

(\frac{12}{7} x^{3 m - (\frac{1}{3})})^{3} (\frac{7}{12} x^{\frac{1}{3}})^{3}

Simplify

(\frac{12}{7} x^{3 m - (\frac{1}{3})})^{3} : \frac{1728 x ^{9 m - 1}}{343}

= \frac{1728 x ^{9 m - 1}}{343} (\frac{7}{12} x^{\frac{1}{3}})^{3}

Simplify

(\frac{7}{12} x^{\frac{1}{3}})^{3} : \frac{343 x}{1728}

= \frac{1728 x ^{9 m - 1}}{343} \cdot \frac{343 x}{1728}

Apply the fraction rule:

\frac{a}{b} \cdot \frac{c}{d} = \frac{a \cdot c}{b \cdot d}

= \frac{1728 x ^{9 m - 1} \cdot 343 x}{343 \cdot 1728}

Cancel

\frac{1728 x ^{9 m - 1} \cdot 343 x}{343 \cdot 1728} : x^{9 m - 1} x

= x^{9 m - 1} x

Apply exponent rule:

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

x^{9 m - 1} x = x^{9 m - 1 + 1}

= x^{9 m - 1 + 1}

- 1 + 1 = 0

= x^{9 m}

(5 - 2)^{2} - z = (1 - 20)^{2}

e^{1}

4 x^{2} - 3 = 0

(x + 4)^{2} = 0

What is (12/7 x^{3m-(1/3)})^3*(7/12 x^{(1/3)})^3 ?
The solution to (12/7 x^{3m-(1/3)})^3*(7/12 x^{(1/3)})^3 is x^{9m}