Solve (-5x^-2y^3)^-2

$$( - 5 x ^ { - 2 } y ^ { 3 } ) ^ { - 2 }$$

Evaluate

$$\frac{x^{4}}{25y^{6}}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(-5x^{-2}y^{3}\right)^{-2}$$

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

$$\left(-5\right)^{-2}\left(x^{-2}\right)^{-2}\left(y^{3}\right)^{-2}$$

Raise -5 to the power -2.

$$\frac{1}{25}\left(x^{-2}\right)^{-2}\left(y^{3}\right)^{-2}$$

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

$$\frac{1}{25}x^{-2\left(-2\right)}y^{3\left(-2\right)}$$

Multiply -2 times -2.

$$\frac{1}{25}x^{4}y^{3\left(-2\right)}$$

Multiply 3 times -2.

$$\frac{1}{25}x^{4}\times \frac{1}{y^{6}}$$

Expand

$$\frac{x^{4}}{25y^{6}}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(-5x^{-2}y^{3}\right)^{-2}$$

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

$$\left(-5\right)^{-2}\left(x^{-2}\right)^{-2}\left(y^{3}\right)^{-2}$$

Raise -5 to the power -2.

$$\frac{1}{25}\left(x^{-2}\right)^{-2}\left(y^{3}\right)^{-2}$$

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

$$\frac{1}{25}x^{-2\left(-2\right)}y^{3\left(-2\right)}$$

Multiply -2 times -2.

$$\frac{1}{25}x^{4}y^{3\left(-2\right)}$$

Multiply 3 times -2.

$$\frac{1}{25}x^{4}\times \frac{1}{y^{6}}$$