Solve (3x^-6y^5)^-3

$$( 3 x ^ { - 6 } y ^ { 5 } ) ^ { - 3 }$$

Evaluate

$$\frac{x^{18}}{27y^{15}}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(3x^{-6}y^{5}\right)^{-3}$$

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

$$3^{-3}\left(x^{-6}\right)^{-3}\left(y^{5}\right)^{-3}$$

Raise 3 to the power -3.

$$\frac{1}{27}\left(x^{-6}\right)^{-3}\left(y^{5}\right)^{-3}$$

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

$$\frac{1}{27}x^{-6\left(-3\right)}y^{5\left(-3\right)}$$

Multiply -6 times -3.

$$\frac{1}{27}x^{18}y^{5\left(-3\right)}$$

Multiply 5 times -3.

$$\frac{1}{27}x^{18}\times \frac{1}{y^{15}}$$

Expand

$$\frac{x^{18}}{27y^{15}}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(3x^{-6}y^{5}\right)^{-3}$$

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

$$3^{-3}\left(x^{-6}\right)^{-3}\left(y^{5}\right)^{-3}$$

Raise 3 to the power -3.

$$\frac{1}{27}\left(x^{-6}\right)^{-3}\left(y^{5}\right)^{-3}$$

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

$$\frac{1}{27}x^{-6\left(-3\right)}y^{5\left(-3\right)}$$

Multiply -6 times -3.

$$\frac{1}{27}x^{18}y^{5\left(-3\right)}$$

Multiply 5 times -3.

$$\frac{1}{27}x^{18}\times \frac{1}{y^{15}}$$