Solve (8c^{4}d^2)^2*(2c^3d)^2

$$( 8 c ^ { 4 } d ^ { 2 } ) ^ { 2 } \cdot ( 2 c ^ { 3 } d ) ^ { 2 }$$

Evaluate

$$256d^{6}c^{14}$$

Solution Steps

Expand \left(8c^{4}d^{2}\right)^{2}.

$$8^{2}\left(c^{4}\right)^{2}\left(d^{2}\right)^{2}\times \left(2c^{3}d\right)^{2}$$

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

$$8^{2}c^{8}\left(d^{2}\right)^{2}\times \left(2c^{3}d\right)^{2}$$

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

$$8^{2}c^{8}d^{4}\times \left(2c^{3}d\right)^{2}$$

Calculate 8 to the power of 2 and get 64.

$$64c^{8}d^{4}\times \left(2c^{3}d\right)^{2}$$

Expand \left(2c^{3}d\right)^{2}.

$$64c^{8}d^{4}\times 2^{2}\left(c^{3}\right)^{2}d^{2}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

$$64c^{8}d^{4}\times 2^{2}c^{6}d^{2}$$

Calculate 2 to the power of 2 and get 4.

$$64c^{8}d^{4}\times 4c^{6}d^{2}$$

Multiply 64 and 4 to get 256.

$$256c^{8}d^{4}c^{6}d^{2}$$

To multiply powers of the same base, add their exponents. Add 8 and 6 to get 14.

$$256c^{14}d^{4}d^{2}$$

To multiply powers of the same base, add their exponents. Add 4 and 2 to get 6.

$$256c^{14}d^{6}$$

Expand

$$256d^{6}c^{14}$$

Solution Steps

Expand \left(8c^{4}d^{2}\right)^{2}.

$$8^{2}\left(c^{4}\right)^{2}\left(d^{2}\right)^{2}\times \left(2c^{3}d\right)^{2}$$

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

$$8^{2}c^{8}\left(d^{2}\right)^{2}\times \left(2c^{3}d\right)^{2}$$

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

$$8^{2}c^{8}d^{4}\times \left(2c^{3}d\right)^{2}$$

Calculate 8 to the power of 2 and get 64.

$$64c^{8}d^{4}\times \left(2c^{3}d\right)^{2}$$

Expand \left(2c^{3}d\right)^{2}.

$$64c^{8}d^{4}\times 2^{2}\left(c^{3}\right)^{2}d^{2}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

$$64c^{8}d^{4}\times 2^{2}c^{6}d^{2}$$

Calculate 2 to the power of 2 and get 4.

$$64c^{8}d^{4}\times 4c^{6}d^{2}$$

Multiply 64 and 4 to get 256.

$$256c^{8}d^{4}c^{6}d^{2}$$

To multiply powers of the same base, add their exponents. Add 8 and 6 to get 14.

$$256c^{14}d^{4}d^{2}$$

To multiply powers of the same base, add their exponents. Add 4 and 2 to get 6.

$$256c^{14}d^{6}$$