[((5x^8)/(4y^7))^5]*[(4^4y^2)/(5^2x^-2)]
To simplify the expression, let's break it down step by step:
Step 1: Simplify the first part of the expression.
[(5x^8)/(4y^7)]^5 = (5^5 * x^(8*5))/(4^5 * y^(7*5))
= (3125x^40) / (1024y^35)
Step 2: Simplify the second part of the expression.
(4^4 * y^2) / (5^2 * x^-2) = (256y^2) / (25x^-2)
Step 3: Multiply the results from step 1 and step 2.
[(3125x^40) / (1024y^35)] * [(256y^2) / (25x^-2)]
To multiply the fractions, we multiply the numerators together and the denominators together:
= (3125x^40 * 256y^2) / (1024y^35 * 25x^-2)
Step 4: Simplify the expression.
To simplify further, we can simplify the coefficients (3125 * 256) and the variables (x^40 * x^2 and y^2 * y^35):
= (800000x^42y^2) / (262144y^37 / 25x^2)
= (800000 / 262144) * [(x^42 * x^2) / (y^37 * y^2)]
= (25 / 8) * (x^44 / y^39)
Therefore, the simplified form of the expression is:
(25x^44) / (8y^39)