Solve left(4xy^2right)^-1/left(3xy^3right)^-2

$$\frac{ { \left(4x { y }^{ 2 } \right) }^{ -1 } }{ { \left(3x { y }^{ 3 } \right) }^{ -2 } }$$

Evaluate

$$\frac{9xy^{4}}{4}$$

Solution Steps

Expand \left(4xy^{2}\right)^{-1}.

$$\frac{4^{-1}x^{-1}\left(y^{2}\right)^{-1}}{\left(3xy^{3}\right)^{-2}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and -1 to get -2.

$$\frac{4^{-1}x^{-1}y^{-2}}{\left(3xy^{3}\right)^{-2}}$$

Calculate 4 to the power of -1 and get \frac{1}{4}.

$$\frac{\frac{1}{4}x^{-1}y^{-2}}{\left(3xy^{3}\right)^{-2}}$$

Expand \left(3xy^{3}\right)^{-2}.

$$\frac{\frac{1}{4}x^{-1}y^{-2}}{3^{-2}x^{-2}\left(y^{3}\right)^{-2}}$$

To raise a power to another power, multiply the exponents. Multiply 3 and -2 to get -6.

$$\frac{\frac{1}{4}x^{-1}y^{-2}}{3^{-2}x^{-2}y^{-6}}$$

Calculate 3 to the power of -2 and get \frac{1}{9}.

$$\frac{\frac{1}{4}x^{-1}y^{-2}}{\frac{1}{9}x^{-2}y^{-6}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$\frac{\frac{1}{4}x^{1}y^{4}}{\frac{1}{9}}$$

Calculate x to the power of 1 and get x.

$$\frac{\frac{1}{4}xy^{4}}{\frac{1}{9}}$$

Divide \frac{1}{4}xy^{4} by \frac{1}{9} by multiplying \frac{1}{4}xy^{4} by the reciprocal of \frac{1}{9}.

$$\frac{1}{4}xy^{4}\times 9$$

Multiply \frac{1}{4} and 9 to get \frac{9}{4}.

$$\frac{9}{4}xy^{4}$$

Expand

$$\frac{9xy^{4}}{4}$$

Solution Steps

Expand \left(4xy^{2}\right)^{-1}.

$$\frac{4^{-1}x^{-1}\left(y^{2}\right)^{-1}}{\left(3xy^{3}\right)^{-2}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and -1 to get -2.

$$\frac{4^{-1}x^{-1}y^{-2}}{\left(3xy^{3}\right)^{-2}}$$

Calculate 4 to the power of -1 and get \frac{1}{4}.

$$\frac{\frac{1}{4}x^{-1}y^{-2}}{\left(3xy^{3}\right)^{-2}}$$

Expand \left(3xy^{3}\right)^{-2}.

$$\frac{\frac{1}{4}x^{-1}y^{-2}}{3^{-2}x^{-2}\left(y^{3}\right)^{-2}}$$

To raise a power to another power, multiply the exponents. Multiply 3 and -2 to get -6.

$$\frac{\frac{1}{4}x^{-1}y^{-2}}{3^{-2}x^{-2}y^{-6}}$$

Calculate 3 to the power of -2 and get \frac{1}{9}.

$$\frac{\frac{1}{4}x^{-1}y^{-2}}{\frac{1}{9}x^{-2}y^{-6}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$\frac{\frac{1}{4}x^{1}y^{4}}{\frac{1}{9}}$$

Calculate x to the power of 1 and get x.

$$\frac{\frac{1}{4}xy^{4}}{\frac{1}{9}}$$

Divide \frac{1}{4}xy^{4} by \frac{1}{9} by multiplying \frac{1}{4}xy^{4} by the reciprocal of \frac{1}{9}.

$$\frac{1}{4}xy^{4}\times 9$$

Multiply \frac{1}{4} and 9 to get \frac{9}{4}.

$$\frac{9}{4}xy^{4}$$