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

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

Evaluate

$$-\frac{8x^{9}}{y^{15}}$$

Solution Steps

Use the rules of exponents to simplify the expression.

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

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

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

Raise -2 to the power 3.

$$-8\left(x^{3}\right)^{3}\left(y^{-5}\right)^{3}$$

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

$$-8x^{3\times 3}y^{-5\times 3}$$

Multiply 3 times 3.

$$-8x^{9}y^{-5\times 3}$$

Multiply -5 times 3.

$$-8x^{9}\times \frac{1}{y^{15}}$$

Expand

$$-\frac{8x^{9}}{y^{15}}$$

Solution Steps

Use the rules of exponents to simplify the expression.

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

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

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

Raise -2 to the power 3.

$$-8\left(x^{3}\right)^{3}\left(y^{-5}\right)^{3}$$

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

$$-8x^{3\times 3}y^{-5\times 3}$$

Multiply 3 times 3.

$$-8x^{9}y^{-5\times 3}$$

Multiply -5 times 3.

$$-8x^{9}\times \frac{1}{y^{15}}$$