Solve (c^4d^5)^4=

$$( c ^ { 4 } d ^ { 5 } ) ^ { 4 } =$$

Evaluate

$$c^{16}d^{20}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(c^{4}d^{5}\right)^{4}$$

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

$$\left(c^{4}\right)^{4}\left(d^{5}\right)^{4}$$

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

$$c^{4\times 4}d^{5\times 4}$$

Multiply 4 times 4.

$$c^{16}d^{5\times 4}$$

Multiply 5 times 4.

$$c^{16}d^{20}$$

Expand

$$c^{16}d^{20}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(c^{4}d^{5}\right)^{4}$$

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

$$\left(c^{4}\right)^{4}\left(d^{5}\right)^{4}$$

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

$$c^{4\times 4}d^{5\times 4}$$

Multiply 4 times 4.

$$c^{16}d^{5\times 4}$$

Multiply 5 times 4.

$$c^{16}d^{20}$$