What is (5/2)^{10}*((5/4)^5)^{-2} ?

The solution to (5/2)^{10}*((5/4)^5)^{-2} is 1024

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simplify (5/2)^{10}*((5/4)^5)^{-2}

simplify

(\frac{5}{2})^{10} \cdot ((\frac{5}{4})^{5})^{- 2}

1024

Solution steps

(\frac{5}{2})^{10} ((\frac{5}{4})^{5})^{- 2}

(\frac{5}{2})^{10} = \frac{9765625}{1024}

= \frac{9765625}{1024} ((\frac{5}{4})^{5})^{- 2}

Apply exponent rule:

(a^{b})^{c} = a^{b c}, a \geq 0

((\frac{5}{4})^{5})^{- 2} = (\frac{5}{4})^{5 (- 2)}

= \frac{9765625}{1024} (\frac{5}{4})^{5 (- 2)}

5 (- 2) = - 10

= \frac{9765625}{1024} (\frac{5}{4})^{- 10}

Apply exponent rule:

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

(\frac{5}{4})^{- 10} = \frac{1}{( \frac{5}{4} ) ^{10}}

= \frac{9765625}{1024} \cdot \frac{1}{( \frac{5}{4} ) ^{10}}

(\frac{5}{4})^{10} = \frac{9765625}{1048576}

= \frac{9765625}{1024} \cdot \frac{1}{\frac{9765625}{1048576}}

Apply the fraction rule:

\frac{1}{\frac{b}{c}} = \frac{c}{b}

= \frac{9765625}{1024} \cdot \frac{1048576}{9765625}

Cross-cancel common factor:

9765625

= \frac{1048576}{1024}

Cancel

\frac{1048576}{1024} : 1024

= 1024

3 x^{2} + 6 x - 6 = 0

w^{5} x^{5} y^{5} - w x^{4} y^{5}

2 x^{2} + 9 x + 10 = 0

16378 = \frac{x ^{2}}{398600}

2 x^{2} - 9 x - 5

What is (5/2)^{10}*((5/4)^5)^{-2} ?
The solution to (5/2)^{10}*((5/4)^5)^{-2} is 1024