The expression ( x^4y^4 )^4 ( xy^4 )^−4 OVER x^4 * y^6 equals x^e OVER y^d where...

Question

the exponent e of x is ____ and the exponent d of y is ____

Answer 1

Assuming e is a variable, and not the number e

[ (x⁴y⁴)⁴(xy⁴)^-4 ] / (x⁴y⁶) = x^e/y^d

Exponent Rules:

x^a·x^b = x^a+b

x^a/x^b = x^a-b

(x^a)^b = x^a·b

Apply the exponent rules to the left side in order to simplify:

[ x¹⁶y¹⁶x^-4y^-16 ] / (x⁴y⁶) = x^e/y^d

(x¹⁶x^-4)/x⁴ · (y¹⁶y^-16 ) /y⁶ = x^e/y^d

x^{(16 + -4 - 4)} · y^{(16 + -16 - 6)} = x^e/y^d

x⁸·y^-6 = x^e/y^d

x⁸/y⁶ = x^e/y^d

Since both sides are equal, by comparison of both sides, the exponent e is equal to 8 and the exponent d is equal to 6