Solve c^{2}d^2x(-5c^3d^3)^2

$$c ^ { 2 } d ^ { 2 } x ( - 5 c ^ { 3 } d ^ { 3 } ) ^ { 2 }$$

Evaluate

$$25x\left(cd\right)^{8}$$

Solution Steps

Expand \left(-5c^{3}d^{3}\right)^{2}.

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

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

$$c^{2}d^{2}x\left(-5\right)^{2}c^{6}\left(d^{3}\right)^{2}$$

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

$$c^{2}d^{2}x\left(-5\right)^{2}c^{6}d^{6}$$

Calculate -5 to the power of 2 and get 25.

$$c^{2}d^{2}x\times 25c^{6}d^{6}$$

To multiply powers of the same base, add their exponents. Add 2 and 6 to get 8.

$$c^{8}d^{2}x\times 25d^{6}$$

To multiply powers of the same base, add their exponents. Add 2 and 6 to get 8.

$$c^{8}d^{8}x\times 25$$

Expand

$$25x\left(cd\right)^{8}$$

Solution Steps

Expand \left(-5c^{3}d^{3}\right)^{2}.

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

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

$$c^{2}d^{2}x\left(-5\right)^{2}c^{6}\left(d^{3}\right)^{2}$$

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

$$c^{2}d^{2}x\left(-5\right)^{2}c^{6}d^{6}$$

Calculate -5 to the power of 2 and get 25.

$$c^{2}d^{2}x\times 25c^{6}d^{6}$$

To multiply powers of the same base, add their exponents. Add 2 and 6 to get 8.

$$c^{8}d^{2}x\times 25d^{6}$$

To multiply powers of the same base, add their exponents. Add 2 and 6 to get 8.

$$c^{8}d^{8}x\times 25$$