Simplify ((3x^((3)/(2))y^(3))/(x^(2)y^(-(1)/(2))))^(-2)

Question

Simplify  ((3x^((3)/(2))y^(3))/(x^(2)y^(-(1)/(2))))^(-2)

Bytelearn · Accepted Answer

Rewrite with negative exponent: Rewrite the expression with negative exponent outside the parentheses. The negative exponent indicates that we should take the reciprocal of the base. In this case, the base is the entire fraction inside the parentheses.Apply negative exponent to fraction: Apply the negative exponent to both the numerator and the denominator of the fraction. When an entire fraction is raised to a negative exponent, we flip the fraction and change the sign of the exponent to positive. ((3x^(3/2)y^3)/(x^2y^(-1/2)))^(-2) becomes (x^2y^(-1/2))/(3x^(3/2)y^3))^2Apply exponent to terms: Apply the exponent to each term inside the parentheses. When raising a fraction to an exponent, we raise both the numerator and the denominator to that exponent. (x^2y^(-1/2))^2/(3x^(3/2)y^3)^2Simplify using power rule: Simplify the expression by applying the power to power rule. The power to power rule states that (a^m)^n = a^(m*n). We apply this rule to each term in the numerator and the denominator. (x^(2*2)y^((-1/2)*2))/(3^2x^((3/2)*2)y^(3*2))Perform exponent multiplication: Perform the multiplication of the exponents. Now we multiply the exponents to simplify the expression further. x^(4)y^(-1)/(9x^3y^6)Combine like terms: Combine the like terms by subtracting the exponents. When dividing terms with the same base, we subtract the exponents. x^(4-3)y^(-1-6)/9Perform exponent subtraction: Simplify the expression by performing the subtraction of the exponents. Now we subtract the exponents to get the final simplified form. x^(1)y^(-7)/9Rewrite with positive exponents: Rewrite the expression with positive exponents. Negative exponents indicate that the term is on the wrong side of the fraction line, so we move them to the other side to make the exponents positive. x/9y^7

Simplify $\left(\frac{3x^{\frac{3}{2}}y^{3}}{x^{2}y^{-\frac{1}{2}}}\right)^{-2}$

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Simplify $\left(\frac{3x^{\frac{3}{2}}y^{3}}{x^{2}y^{-\frac{1}{2}}}\right)^{-2}$