Solve (-4d^5)^2(8d^4c^6)

$$( - 4 d ^ { 5 } ) ^ { 2 } ( 8 d ^ { 4 } c ^ { 6 } )$$

Evaluate

$$128c^{6}d^{14}$$

Solution Steps

Expand \left(-4d^{5}\right)^{2}.

$$\left(-4\right)^{2}\left(d^{5}\right)^{2}\times 8d^{4}c^{6}$$

To raise a power to another power, multiply the exponents. Multiply 5 and 2 to get 10.

$$\left(-4\right)^{2}d^{10}\times 8d^{4}c^{6}$$

Calculate -4 to the power of 2 and get 16.

$$16d^{10}\times 8d^{4}c^{6}$$

Multiply 16 and 8 to get 128.

$$128d^{10}d^{4}c^{6}$$

To multiply powers of the same base, add their exponents. Add 10 and 4 to get 14.

$$128d^{14}c^{6}$$

Expand

$$128c^{6}d^{14}$$

Solution Steps

Expand \left(-4d^{5}\right)^{2}.

$$\left(-4\right)^{2}\left(d^{5}\right)^{2}\times 8d^{4}c^{6}$$

To raise a power to another power, multiply the exponents. Multiply 5 and 2 to get 10.

$$\left(-4\right)^{2}d^{10}\times 8d^{4}c^{6}$$

Calculate -4 to the power of 2 and get 16.

$$16d^{10}\times 8d^{4}c^{6}$$

Multiply 16 and 8 to get 128.

$$128d^{10}d^{4}c^{6}$$

To multiply powers of the same base, add their exponents. Add 10 and 4 to get 14.

$$128d^{14}c^{6}$$