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

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

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

simplify

(\frac{5}{2})^{10} l e f t ((\frac{5}{4})^{5})^{- 2}

1024 e l f t

Solution steps

(\frac{5}{2})^{10} l e f t ((\frac{5}{4})^{5})^{- 2}

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

= (\frac{5}{2})^{10} l e f t (\frac{5}{4})^{- 10}

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

= e (\frac{5}{4})^{- 10} \frac{5 ^{10}}{2 ^{10}} l f t

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

= e \frac{5 ^{10}}{2 ^{10}} \cdot \frac{4 ^{10}}{5 ^{10}} l f t

Multiply fractions:

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

= \frac{5 ^{10} \cdot 4 ^{10} l e f t}{2 ^{10} \cdot 5 ^{10}}

Cancel the common factor:

5^{10}

= \frac{4 ^{10} l e f t}{2 ^{10}}

Factor

4^{10} : 2^{20}

= \frac{2 ^{20} e l f t}{2 ^{10}}

Cancel

\frac{2 ^{20} l e f t}{2 ^{10}} : 2^{10} e l f t

= 2^{10} e l f t

2^{10} = 1024

= 1024 e l f t

32

(3 x^{2} y^{3}) (7 x y^{2})

p^{1} (3 - 4) p^{2} (- 4.7)

- \frac{x ^{5}}{y ^{5}}

(v^{6} w^{3}) (v^{9} w)

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