Simplify \( (\frac{b^{4x-3y}}{b^{3x+2y}})^{x} (\frac{b^{3x+6y}}{b^{-2x+4y}})^y\)

Solution

• \( (\frac{b^{4x-3y}}{b^{3x+2y}})^{x} (\frac{b^{3x+6y}}{b^{-2x+4y}})^y\) = \( (\frac{b^{4x}b^{-3y}}{b^{3x}b^{2y}})^x (\frac{b^{3x}b^{6y}}{b^{-2x}b^{4y}})^y\)

• = \( (\frac{b^x}{b^5y})^x (b^{5x}b^{2y})^y\)

• = \( (\frac{b^{x^2}}{b^{5xy}}) (b^{5xy}b^{2y^2})\)

• = \( b^{x^2 +2y^2}\)