Solve (2x^3y^-7)^-3

$$( 2 x ^ { 3 } y ^ { - 7 } ) ^ { - 3 }$$

Evaluate

$$\frac{y^{21}}{8x^{9}}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(2x^{3}y^{-7}\right)^{-3}$$

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

$$2^{-3}\left(x^{3}\right)^{-3}\left(y^{-7}\right)^{-3}$$

Raise 2 to the power -3.

$$\frac{1}{8}\left(x^{3}\right)^{-3}\left(y^{-7}\right)^{-3}$$

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

$$\frac{1}{8}x^{3\left(-3\right)}y^{-7\left(-3\right)}$$

Multiply 3 times -3.

$$\frac{1}{8}\times \frac{1}{x^{9}}y^{-7\left(-3\right)}$$

Multiply -7 times -3.

$$\frac{1}{8}\times \frac{1}{x^{9}}y^{21}$$

Expand

$$\frac{y^{21}}{8x^{9}}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(2x^{3}y^{-7}\right)^{-3}$$

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

$$2^{-3}\left(x^{3}\right)^{-3}\left(y^{-7}\right)^{-3}$$

Raise 2 to the power -3.

$$\frac{1}{8}\left(x^{3}\right)^{-3}\left(y^{-7}\right)^{-3}$$

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

$$\frac{1}{8}x^{3\left(-3\right)}y^{-7\left(-3\right)}$$

Multiply 3 times -3.

$$\frac{1}{8}\times \frac{1}{x^{9}}y^{-7\left(-3\right)}$$

Multiply -7 times -3.

$$\frac{1}{8}\times \frac{1}{x^{9}}y^{21}$$