Solve frac{(c^{2}d^-1)^-3}{c^-4d^5}

$$\frac { ( c ^ { 2 } d ^ { - 1 } ) ^ { - 3 } } { c ^ { - 4 } d ^ { 5 } }$$

Evaluate

$$\frac{1}{\left(cd\right)^{2}}$$

Steps Using Product of Powers Property

Use the rules of exponents to simplify the expression.

$$\left(c^{2}\times \frac{1}{d}\right)^{-3}\times \frac{1}{c^{-4}d^{5}}$$

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

$$\left(c^{2}\right)^{-3}\times \left(\frac{1}{d}\right)^{-3}\times \frac{1}{c^{-4}}\times \frac{1}{d^{5}}$$

Use the Commutative Property of Multiplication.

$$\left(c^{2}\right)^{-3}\times \frac{1}{c^{-4}}\times \left(\frac{1}{d}\right)^{-3}\times \frac{1}{d^{5}}$$

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

$$c^{2\left(-3\right)}c^{-4\left(-1\right)}d^{-\left(-3\right)}d^{5\left(-1\right)}$$

Multiply 2 times -3.

$$c^{-6}c^{-4\left(-1\right)}d^{-\left(-3\right)}d^{5\left(-1\right)}$$

Multiply -4 times -1.

$$c^{-6}c^{4}d^{-\left(-3\right)}d^{5\left(-1\right)}$$

Multiply -1 times -3.

$$c^{-6}c^{4}d^{3}d^{5\left(-1\right)}$$

Multiply 5 times -1.

$$c^{-6}c^{4}d^{3}d^{-5}$$

To multiply powers of the same base, add their exponents.

$$c^{-6+4}d^{3-5}$$

Add the exponents -6 and 4.

$$c^{-2}d^{3-5}$$

Add the exponents 3 and -5.

$$c^{-2}d^{-2}$$

Expand

$$\frac{1}{\left(cd\right)^{2}}$$

Steps Using Product of Powers Property

Use the rules of exponents to simplify the expression.

$$\left(c^{2}\times \frac{1}{d}\right)^{-3}\times \frac{1}{c^{-4}d^{5}}$$

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

$$\left(c^{2}\right)^{-3}\times \left(\frac{1}{d}\right)^{-3}\times \frac{1}{c^{-4}}\times \frac{1}{d^{5}}$$

Use the Commutative Property of Multiplication.

$$\left(c^{2}\right)^{-3}\times \frac{1}{c^{-4}}\times \left(\frac{1}{d}\right)^{-3}\times \frac{1}{d^{5}}$$

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

$$c^{2\left(-3\right)}c^{-4\left(-1\right)}d^{-\left(-3\right)}d^{5\left(-1\right)}$$

Multiply 2 times -3.

$$c^{-6}c^{-4\left(-1\right)}d^{-\left(-3\right)}d^{5\left(-1\right)}$$

Multiply -4 times -1.

$$c^{-6}c^{4}d^{-\left(-3\right)}d^{5\left(-1\right)}$$

Multiply -1 times -3.

$$c^{-6}c^{4}d^{3}d^{5\left(-1\right)}$$

Multiply 5 times -1.

$$c^{-6}c^{4}d^{3}d^{-5}$$

To multiply powers of the same base, add their exponents.

$$c^{-6+4}d^{3-5}$$

Add the exponents -6 and 4.

$$c^{-2}d^{3-5}$$

Add the exponents 3 and -5.

$$c^{-2}d^{-2}$$