What is (1 5/7 x^{2n-2/3})^6*(7/12 x^{1/3})^6 ?

The solution to (1 5/7 x^{2n-2/3})^6*(7/12 x^{1/3})^6 is x^{12n-2}

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simplify (1 5/7 x^{2n-2/3})^6*(7/12 x^{1/3})^6

simplify

(1 \frac{5}{7} x^{2 n - \frac{2}{3}})^{6} \cdot (\frac{7}{12} x^{\frac{1}{3}})^{6}

x^{12 n - 2}

Solution steps

(1 \frac{5}{7} x^{2 n - \frac{2}{3}})^{6} \cdot (\frac{7}{12} x^{\frac{1}{3}})^{6}

Convert mixed numbers to improper fractions:

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

= (\frac{12}{7} x^{2 n - \frac{2}{3}})^{6} \cdot (\frac{7}{12} x^{\frac{1}{3}})^{6}

Simplify

(\frac{12}{7} x^{2 n - \frac{2}{3}})^{6} : \frac{2985984 x ^{2 (6 n - 2)}}{117649}

= \frac{2985984 x ^{2 (6 n - 2)}}{117649} (\frac{7}{12} x^{\frac{1}{3}})^{6}

Simplify

(\frac{7}{12} x^{\frac{1}{3}})^{6} : \frac{117649 x ^{2}}{2985984}

= \frac{2985984 x ^{2 (6 n - 2)}}{117649} \cdot \frac{117649 x ^{2}}{2985984}

Apply the fraction rule:

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

= \frac{2985984 x ^{2 (6 n - 2)} \cdot 117649 x ^{2}}{117649 \cdot 2985984}

Cancel

\frac{2985984 x ^{2 (6 n - 2)} \cdot 117649 x ^{2}}{117649 \cdot 2985984} : x^{2 (6 n - 2)} x^{2}

= x^{2 (6 n - 2)} x^{2}

Apply exponent rule:

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

x^{2 (6 n - 2)} x^{2} = x^{2 (6 n - 2) + 2}

= x^{2 (6 n - 2) + 2}

Simplify

2 (6 n - 2) + 2 : 12 n - 2

= x^{12 n - 2}

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What is (1 5/7 x^{2n-2/3})^6*(7/12 x^{1/3})^6 ?
The solution to (1 5/7 x^{2n-2/3})^6*(7/12 x^{1/3})^6 is x^{12n-2}