Question

evaluate (5/8)^-7*(8/5)^-4

Answer 1

Answer:

(8³)*(5-³ )

Step-by-step explanation:

(5/8)^-7*(8/5)^-4

=(8/5)⁷ * (5/8)⁴

=(8⁷*5⁴)/(5⁷*8⁴)

=(8⁷-⁴)*(5⁴-⁷)

=(8³)*(5-³ )

Answer 2

Given:

A mathematical expression (5/8)^-7 x (8/5)^-4.

To Find:

The value of the above expression is?

Solution:

1. The formulae used to solve the given problem are,

• $(\frac{1}{a})^{-n} = a^n$,
• $a^n = (a*a*a*a..*a)$ ( a repeated n times )
• $\frac{a^m}{a^n} = a^{m-n}$

2. The given expression is$(\frac{5}{8})^{-7}*(\frac{8}{5} )^{-4}$,

=>$(\frac{8}{5})^{+7}*(\frac{5}{8} )^{+4}$,

=>$\frac{8^7}{5^7} *\frac{5^4}{8^4}$,

=>$\frac{8^{(7-4)}}{5^{(7-4)}}$,

=>$\frac{8^3}{5^3}$,

=> (512/125),

=> 4.096.

Therefore, the value of the expression$(\frac{5}{8})^{-7}*(\frac{8}{5} )^{-4}$ is 4.096 (OR) 512/125.