Solve (3x^10y^-8)^-6

$$( 3 x ^ { 10 } y ^ { - 8 } ) ^ { - 6 }$$

Evaluate

$$\frac{y^{48}}{729x^{60}}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(3x^{10}y^{-8}\right)^{-6}$$

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

$$3^{-6}\left(x^{10}\right)^{-6}\left(y^{-8}\right)^{-6}$$

Raise 3 to the power -6.

$$\frac{1}{729}\left(x^{10}\right)^{-6}\left(y^{-8}\right)^{-6}$$

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

$$\frac{1}{729}x^{10\left(-6\right)}y^{-8\left(-6\right)}$$

Multiply 10 times -6.

$$\frac{1}{729}\times \frac{1}{x^{60}}y^{-8\left(-6\right)}$$

Multiply -8 times -6.

$$\frac{1}{729}\times \frac{1}{x^{60}}y^{48}$$

Expand

$$\frac{y^{48}}{729x^{60}}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(3x^{10}y^{-8}\right)^{-6}$$

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

$$3^{-6}\left(x^{10}\right)^{-6}\left(y^{-8}\right)^{-6}$$

Raise 3 to the power -6.

$$\frac{1}{729}\left(x^{10}\right)^{-6}\left(y^{-8}\right)^{-6}$$

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

$$\frac{1}{729}x^{10\left(-6\right)}y^{-8\left(-6\right)}$$

Multiply 10 times -6.

$$\frac{1}{729}\times \frac{1}{x^{60}}y^{-8\left(-6\right)}$$

Multiply -8 times -6.

$$\frac{1}{729}\times \frac{1}{x^{60}}y^{48}$$