Simplify. a. ((x^(6)y^(4))^((3)/(2)))/((x^(-3)y^(-(1)/(2)))^((2)/(3)))(x^(9)y^(6))/(x^(-2)y^(-(1)/(3)))

Question

Simplify. a.  ((x^(6)y^(4))^((3)/(2)))/((x^(-3)y^(-(1)/(2)))^((2)/(3)))(x^(9)y^(6))/(x^(-2)y^(-(1)/(3)))

Bytelearn · Accepted Answer

Simplify first part: First, we will simplify each part of the expression separately using the properties of exponents. For the first part, ((x^(6)y^(4))^((3)/(2))), we apply the power of a power rule, which states that (a^m)^n = a^(m*n). ((x^(6)y^(4))^((3)/(2))) = x^(6*(3/2)) * y^(4*(3/2)) = x^9 * y^6Simplify second part: For the second part, ((x^(-3)y^(-(1)/(2)))^((2)/(3))), we again apply the power of a power rule. ((x^(-3)y^(-(1)/(2)))^((2)/(3))) = x^(-3*(2/3)) * y^(-(1/2)*(2/3)) = x^(-2) * y^(-(1/3))Simplify third part: For the third part, (x^(9)y^(6))/(x^(-2)y^(-(1)/(3))), we use the quotient of powers rule, which states that a^m / a^n = a^(m-n). (x^(9)y^(6))/(x^(-2)y^(-(1)/(3))) = x^(9-(-2)) * y^(6-(-(1/3))) = x^(11) * y^(6+(1/3)) = x^(11) * y^(19/3)Combine simplified parts: Now we will combine the simplified parts of the expression. ((x^9 * y^6) / (x^(-2) * y^(-(1/3)))) * (x^(11) * y^(19/3)) = x^(9+2) * y^(6+1/3) * x^(11) * y^(19/3)Combine like terms: We combine like terms by adding the exponents of the same base. x^(9+2+11) * y^(6+1/3+19/3) = x^(22) * y^(6+20/3) = x^(22) * y^(18/3+20/3) = x^(22) * y^(38/3)Final simplification: Finally, we simplify the exponent for y by adding the fractions. y^(18/3+20/3) = y^(38/3)

Simplify. $\newline$ a. $\frac{(x^{6}y^{4})^{\frac{3}{2}}}{(x^{-3}y^{-\frac{1}{2}})^{\frac{2}{3}}}(x^{9}y^{6})\div(x^{-2}y^{-\frac{1}{3}})$

Full solution

More problems from Find derivatives of using multiple formulae

Related topics

Simplify.\newlinea. (x6y4)32(x−3y−12)23(x9y6)÷(x−2y−13)\frac{(x^{6}y^{4})^{\frac{3}{2}}}{(x^{-3}y^{-\frac{1}{2}})^{\frac{2}{3}}}(x^{9}y^{6})\div(x^{-2}y^{-\frac{1}{3}})(x−3y−21​)32​(x6y4)23​​(x9y6)÷(x−2y−31​)

Simplify. $\newline$ a. $\frac{(x^{6}y^{4})^{\frac{3}{2}}}{(x^{-3}y^{-\frac{1}{2}})^{\frac{2}{3}}}(x^{9}y^{6})\div(x^{-2}y^{-\frac{1}{3}})$