Implied the exponential expression Write the result using on

Implied the exponential expression. Write the result using only positive exponent. (x^3y^3/x^4y^-3)^2 y^25/y y^7/x^2 y^19/x^2.

Solution

16 ) Given that

[ (x³y²) / x⁴y^-3) ]² = ( x⁶y⁴ ) / ( x⁸y^-6) [ since ( a/b )^m = a^m/b^m ]

= x^6-8.y^{4- (-6)} [ since a^m/aⁿ = a^m-n ]

= x^-2y¹⁰ [ since x^-a = 1/x^a ]

= y¹⁰ / x²

Therefore,

   [ (x³y²) / x⁴y^-3) ]² = y¹⁰ / x²