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True [87]
3 years ago
12

Pls solve this plèeeeeeeeease

Mathematics
1 answer:
gtnhenbr [62]3 years ago
3 0

Answer:

\dfrac{5^7}{2} = \dfrac{78125}{2}

Step-by-step explanation:

\left( \dfrac{4}{5} \right)^2 \times 5^4 \times \left( \dfrac{2}{5} \right)^{-2} \div \left( \dfrac{5}{2} \right)^{-3} =

= \dfrac{4^2}{5^2} \times 5^4 \times \dfrac{5^2}{2^2} \times \dfrac{5^3}{2^3}

= \dfrac{(2^2)^2}{5^2} \times 5^4 \times \dfrac{5^2}{2^2} \times \dfrac{5^3}{2^3}

= \dfrac{2^4}{5^2} \times 5^4 \times \dfrac{5^2}{2^2} \times \dfrac{5^3}{2^3}

= 2^{4 - 2 - 3} \times 5^{- 2 + 4 + 2 + 3}

= 2^{-1} \times 5^{7}

= \dfrac{5^7}{2}

= \dfrac{78125}{2}

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