What is (1 5/7 x^{3m-1/3})^3*(7/12 x^{1/3})^3 ?

The solution to (1 5/7 x^{3m-1/3})^3*(7/12 x^{1/3})^3 is x^{9m}

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simplify (1 5/7 x^{3m-1/3})^3*(7/12 x^{1/3})^3

simplify

(1 \frac{5}{7} x^{3 m - \frac{1}{3}})^{3} \cdot (\frac{7}{12} x^{\frac{1}{3}})^{3}

x^{9 m}

Solution steps

(1 \frac{5}{7} x^{3 m - \frac{1}{3}})^{3} \cdot (\frac{7}{12} x^{\frac{1}{3}})^{3}

Convert mixed numbers to improper fractions:

1 \frac{5}{7} = \frac{12}{7}

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

81 \cdot 900

- 12 \cdot 4

5 \cdot \frac{4}{5}

5^{- \frac{1}{3}}

(x - 2) (x^{2} + 1)

What is (1 5/7 x^{3m-1/3})^3*(7/12 x^{1/3})^3 ?
The solution to (1 5/7 x^{3m-1/3})^3*(7/12 x^{1/3})^3 is x^{9m}