Solve (6cd^-1)^-3

$$( 6 c d ^ { - 1 } ) ^ { - 3 }$$

Evaluate

$$\frac{\left(\frac{d}{c}\right)^{3}}{216}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(6c^{1}\times \frac{1}{d}\right)^{-3}$$

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

$$6^{-3}\left(c^{1}\right)^{-3}\times \left(\frac{1}{d}\right)^{-3}$$

Raise 6 to the power -3.

$$\frac{1}{216}\left(c^{1}\right)^{-3}\times \left(\frac{1}{d}\right)^{-3}$$

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

$$\frac{1}{216}c^{-3}d^{-\left(-3\right)}$$

Multiply -1 times -3.

$$\frac{1}{216}\times \frac{1}{c^{3}}d^{3}$$

Expand

$$\frac{\left(\frac{d}{c}\right)^{3}}{216}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(6c^{1}\times \frac{1}{d}\right)^{-3}$$

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

$$6^{-3}\left(c^{1}\right)^{-3}\times \left(\frac{1}{d}\right)^{-3}$$

Raise 6 to the power -3.

$$\frac{1}{216}\left(c^{1}\right)^{-3}\times \left(\frac{1}{d}\right)^{-3}$$

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

$$\frac{1}{216}c^{-3}d^{-\left(-3\right)}$$

Multiply -1 times -3.

$$\frac{1}{216}\times \frac{1}{c^{3}}d^{3}$$