Solve (x^{-3}y^-1)^-2(x^2y)^-1

$$( x ^ { - 3 } y ^ { - 1 } ) ^ { - 2 } ( x ^ { 2 } y ) ^ { - 1 }$$

Evaluate

$$yx^{4}$$

Steps Using Product of Powers Property

Use the rules of exponents to simplify the expression.

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

To raise the product of two or more numbers to a power, raise each number to the power and take their product.

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

Use the Commutative Property of Multiplication.

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

To raise a power to another power, multiply the exponents.

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

Multiply -3 times -2.

$$x^{6}x^{2\left(-1\right)}y^{-\left(-2\right)}\times \frac{1}{y}$$

Multiply 2 times -1.

$$x^{6}x^{-2}y^{-\left(-2\right)}\times \frac{1}{y}$$

Multiply -1 times -2.

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

To multiply powers of the same base, add their exponents.

$$x^{6-2}y^{2-1}$$

Add the exponents 6 and -2.

$$x^{4}y^{2-1}$$

Add the exponents 2 and -1.

$$x^{4}y^{1}$$

For any term t, t^{1}=t.

$$x^{4}y$$

Expand

$$yx^{4}$$

Steps Using Product of Powers Property

Use the rules of exponents to simplify the expression.

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

To raise the product of two or more numbers to a power, raise each number to the power and take their product.

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

Use the Commutative Property of Multiplication.

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

To raise a power to another power, multiply the exponents.

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

Multiply -3 times -2.

$$x^{6}x^{2\left(-1\right)}y^{-\left(-2\right)}\times \frac{1}{y}$$

Multiply 2 times -1.

$$x^{6}x^{-2}y^{-\left(-2\right)}\times \frac{1}{y}$$

Multiply -1 times -2.

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

To multiply powers of the same base, add their exponents.

$$x^{6-2}y^{2-1}$$

Add the exponents 6 and -2.

$$x^{4}y^{2-1}$$

Add the exponents 2 and -1.

$$x^{4}y^{1}$$

For any term t, t^{1}=t.

$$x^{4}y$$