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} ((\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 - 6 ∣ + 9 = 12

6 x + 5 x = - 11

(\frac{8}{3})^{- 2}

- 3 x + 6 \leq 12

- 7 x \leq 28

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