What is \sqrt[3]{((-5)/2)^6}*(2/5)^6*(1/7)^9 ?

The solution to \sqrt[3]{((-5)/2)^6}*(2/5)^6*(1/7)^9 is 16/25221004375

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simplify \sqrt[3]{((-5)/2)^6}(2/5)^6(1/7)^9

simplify

\frac{16}{25221004375}

Decimal Notation

6.34392 E - 10

Solution steps

= \frac{25}{4} (\frac{2}{5})^{6} (\frac{1}{7})^{9}

(\frac{2}{5})^{6} = \frac{64}{15625}

= \frac{25}{4} \cdot \frac{64}{15625} (\frac{1}{7})^{9}

Apply exponent rule:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

(\frac{1}{7})^{9} = \frac{1 ^{9}}{7 ^{9}}

= \frac{25}{4} \cdot \frac{64}{15625} \cdot \frac{1 ^{9}}{7 ^{9}}

1^{9} = 1

= \frac{25}{4} \cdot \frac{64}{15625} \cdot \frac{1}{7 ^{9}}

7^{9} = 40353607

= \frac{25}{4} \cdot \frac{64}{15625} \cdot \frac{1}{40353607}

\frac{64}{15625} = (\frac{25}{4})^{- 3}

= \frac{25}{4} (\frac{25}{4})^{- 3} \frac{1}{40353607}

Apply exponent rule:

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

\frac{25}{4} (\frac{25}{4})^{- 3} = (\frac{25}{4})^{1 - 3}

= (\frac{25}{4})^{1 - 3} \frac{1}{40353607}

Subtract the numbers:

1 - 3 = - 2

= (\frac{25}{4})^{- 2} \frac{1}{40353607}

Apply exponent rule:

a^{- b} = \frac{1}{a ^{b}}

(\frac{25}{4})^{- 2} = \frac{1}{( \frac{25}{4} ) ^{2}}

= \frac{1}{( \frac{25}{4} ) ^{2}} \cdot \frac{1}{40353607}

(\frac{25}{4})^{2} = \frac{625}{16}

= \frac{1}{\frac{625}{16}} \cdot \frac{1}{40353607}

= \frac{1}{40353607} \cdot \frac{1}{\frac{625}{16}}

\frac{1}{\frac{625}{16}} = \frac{16}{625}

= \frac{1}{40353607} \cdot \frac{16}{625}

\frac{1}{40353607} \cdot \frac{16}{625} = \frac{16}{25221004375}

= \frac{16}{25221004375}

81

(1)^{2} e^{- 2 (1)}

7 x

What is \sqrt[3]{((-5)/2)^6}*(2/5)^6*(1/7)^9 ?
The solution to \sqrt[3]{((-5)/2)^6}*(2/5)^6*(1/7)^9 is 16/25221004375