What is (5/9*x^{4n+3/4})^4*(1 4/5*x^{3/2})^4 ?

The solution to (5/9*x^{4n+3/4})^4*(1 4/5*x^{3/2})^4 is x^{16n+9}

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simplify (5/9x^{4n+3/4})^4(1 4/5*x^{3/2})^4

simplify

(\frac{5}{9} \cdot x^{4 n + \frac{3}{4}})^{4} \cdot (1 \frac{4}{5} \cdot x^{\frac{3}{2}})^{4}

x^{16 n + 9}

Solution steps

(\frac{5}{9} \cdot x^{4 n + \frac{3}{4}})^{4} \cdot (1 \frac{4}{5} \cdot x^{\frac{3}{2}})^{4}

Convert mixed numbers to improper fractions:

1 \frac{4}{5} = \frac{9}{5}

= (\frac{5}{9} \cdot x^{4 n + \frac{3}{4}})^{4} \cdot (\frac{9}{5} \cdot x^{\frac{3}{2}})^{4}

Simplify

(\frac{5}{9} x^{4 n + \frac{3}{4}})^{4} : \frac{625 x ^{16 n + 3}}{6561}

= \frac{625 x ^{16 n + 3}}{6561} (\frac{9}{5} x^{\frac{3}{2}})^{4}

Simplify

(\frac{9}{5} x^{\frac{3}{2}})^{4} : \frac{6561 x ^{6}}{625}

= \frac{625 x ^{16 n + 3}}{6561} \cdot \frac{6561 x ^{6}}{625}

Apply the fraction rule:

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

= \frac{625 x ^{16 n + 3} \cdot 6561 x ^{6}}{6561 \cdot 625}

Cancel

\frac{625 x ^{16 n + 3} \cdot 6561 x ^{6}}{6561 \cdot 625} : x^{16 n + 3} x^{6}

= x^{16 n + 3} x^{6}

Apply exponent rule:

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

x^{16 n + 3} x^{6} = x^{16 n + 3 + 6}

= x^{16 n + 3 + 6}

Add the numbers:

3 + 6 = 9

= x^{16 n + 9}

x - x^{- 1}

3 x^{n} - 15 x^{n - 2} - 12 x^{n - 1}

\frac{40 e ^{9}}{5 e ^{8}}

i^{117}

(25)^{\frac{1}{2}} + (8)^{\frac{1}{3}}

What is (5/9*x^{4n+3/4})^4*(1 4/5*x^{3/2})^4 ?
The solution to (5/9*x^{4n+3/4})^4*(1 4/5*x^{3/2})^4 is x^{16n+9}