Solve (2cd^4)^2(cd)^5=

$$( 2 c d ^ { 4 } ) ^ { 2 } ( c d ) ^ { 5 } =$$

Evaluate

$$4c^{7}d^{13}$$

Solution Steps

Expand \left(2cd^{4}\right)^{2}.

$$2^{2}c^{2}\left(d^{4}\right)^{2}\left(cd\right)^{5}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 2 to get 8.

$$2^{2}c^{2}d^{8}\left(cd\right)^{5}$$

Calculate 2 to the power of 2 and get 4.

$$4c^{2}d^{8}\left(cd\right)^{5}$$

Expand \left(cd\right)^{5}.

$$4c^{2}d^{8}c^{5}d^{5}$$

To multiply powers of the same base, add their exponents. Add 2 and 5 to get 7.

$$4c^{7}d^{8}d^{5}$$

To multiply powers of the same base, add their exponents. Add 8 and 5 to get 13.

$$4c^{7}d^{13}$$

Expand

$$4c^{7}d^{13}$$

Solution Steps

Expand \left(2cd^{4}\right)^{2}.

$$2^{2}c^{2}\left(d^{4}\right)^{2}\left(cd\right)^{5}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 2 to get 8.

$$2^{2}c^{2}d^{8}\left(cd\right)^{5}$$

Calculate 2 to the power of 2 and get 4.

$$4c^{2}d^{8}\left(cd\right)^{5}$$

Expand \left(cd\right)^{5}.

$$4c^{2}d^{8}c^{5}d^{5}$$

To multiply powers of the same base, add their exponents. Add 2 and 5 to get 7.

$$4c^{7}d^{8}d^{5}$$

To multiply powers of the same base, add their exponents. Add 8 and 5 to get 13.

$$4c^{7}d^{13}$$