Question

Simplify (5/8)^-7 * (8/5)^-5

Plzplzplzplz

Answer 1

Identities used :

$\bf \: {( \frac{a}{b} )}^{ - m} = {( \frac{b}{a} )}^{m} \\ \\ \bf \frac{ {a}^{m} }{ {a}^{n} } = {a}^{m - n} \\ \\ \bf {a}^{ - m} = \frac{1}{ {a}^{m} }$



${( \frac{5}{8} )}^{ - 7} \times {( \frac{8}{5} )}^{ - 5} \\ \\ = {( \frac{8}{5} )}^{7} \times {( \frac{5}{8} )}^{5} \\ \\ = \frac{ {8}^{7} }{ {5}^{7} } \times \frac{ {5}^{5} }{ {8}^{5} } \\ \\ = \frac{ {8}^{7} \times {5}^{5} }{ {8}^{5} \times {5}^{7} } \\ \\ = {8}^{7 - 5} \times {5}^{5 - 7} \\ \\ = {8}^{2} \times {5}^{ - 2} \\ \\ = 64 \times \frac{1}{25} \\ \\ \bf \: = \frac{64}{25}$

If any doubt, please ask ;)

Answer 2

2.56 is the answer.

Explanation:

( 5/8)^-7 * (8/5)^-5

= (5^-7*8^7) (8^-5* 5^5)

= (5^-7 x 5^5)  (  8^-5 x 8^7)

=  (5^-2)  (  8^2)

=(  8^2)/ (5^2)

=64 /25

= 2.56