What is (2 1/5 a^{5m-3/4})^4*(5/11 a^{5/4})^4 ?

The solution to (2 1/5 a^{5m-3/4})^4*(5/11 a^{5/4})^4 is a^{20m+2}

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simplify (2 1/5 a^{5m-3/4})^4*(5/11 a^{5/4})^4

simplify

(2 \frac{1}{5} a^{5 m - \frac{3}{4}})^{4} \cdot (\frac{5}{11} a^{\frac{5}{4}})^{4}

a^{20 m + 2}

Solution steps

(2 \frac{1}{5} a^{5 m - \frac{3}{4}})^{4} \cdot (\frac{5}{11} a^{\frac{5}{4}})^{4}

Convert mixed numbers to improper fractions:

2 \frac{1}{5} = \frac{11}{5}

= (\frac{11}{5} a^{5 m - \frac{3}{4}})^{4} \cdot (\frac{5}{11} a^{\frac{5}{4}})^{4}

Simplify

(\frac{11}{5} a^{5 m - \frac{3}{4}})^{4} : \frac{14641 a ^{20 m - 3}}{625}

= \frac{14641 a ^{20 m - 3}}{625} (\frac{5}{11} a^{\frac{5}{4}})^{4}

Simplify

(\frac{5}{11} a^{\frac{5}{4}})^{4} : \frac{625 a ^{5}}{14641}

= \frac{14641 a ^{20 m - 3}}{625} \cdot \frac{625 a ^{5}}{14641}

Apply the fraction rule:

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

= \frac{14641 a ^{20 m - 3} \cdot 625 a ^{5}}{625 \cdot 14641}

Cancel

\frac{14641 a ^{20 m - 3} \cdot 625 a ^{5}}{625 \cdot 14641} : a^{20 m - 3} a^{5}

= a^{20 m - 3} a^{5}

Apply exponent rule:

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

a^{20 m - 3} a^{5} = a^{20 m - 3 + 5}

= a^{20 m - 3 + 5}

Add/Subtract the numbers:

- 3 + 5 = 2

= a^{20 m + 2}

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What is (2 1/5 a^{5m-3/4})^4*(5/11 a^{5/4})^4 ?
The solution to (2 1/5 a^{5m-3/4})^4*(5/11 a^{5/4})^4 is a^{20m+2}