Solve -(-2a^{2}bc^{2}d)^3*a^2b^3cd^4

$$- ( - 2 a ^ { 2 } b c ^ { 2 } d ) ^ { 3 } \cdot a ^ { 2 } b ^ { 3 } c d ^ { 4 }$$

Evaluate

$$8b^{6}a^{8}\left(cd\right)^{7}$$

Solution Steps

Expand \left(-2a^{2}bc^{2}d\right)^{3}.

$$\left(-\left(-2\right)^{3}\left(a^{2}\right)^{3}b^{3}\left(c^{2}\right)^{3}d^{3}\right)a^{2}b^{3}cd^{4}$$

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

$$\left(-\left(-2\right)^{3}a^{6}b^{3}\left(c^{2}\right)^{3}d^{3}\right)a^{2}b^{3}cd^{4}$$

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

$$\left(-\left(-2\right)^{3}a^{6}b^{3}c^{6}d^{3}\right)a^{2}b^{3}cd^{4}$$

Calculate -2 to the power of 3 and get -8.

$$\left(-\left(-8a^{6}b^{3}c^{6}d^{3}\right)\right)a^{2}b^{3}cd^{4}$$

The opposite of -8a^{6}b^{3}c^{6}d^{3} is 8a^{6}b^{3}c^{6}d^{3}.

$$8a^{6}b^{3}c^{6}d^{3}a^{2}b^{3}cd^{4}$$

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

$$8a^{8}b^{3}c^{6}d^{3}b^{3}cd^{4}$$

To multiply powers of the same base, add their exponents. Add 3 and 3 to get 6.

$$8a^{8}b^{6}c^{6}d^{3}cd^{4}$$

To multiply powers of the same base, add their exponents. Add 6 and 1 to get 7.

$$8a^{8}b^{6}c^{7}d^{3}d^{4}$$

To multiply powers of the same base, add their exponents. Add 3 and 4 to get 7.

$$8a^{8}b^{6}c^{7}d^{7}$$

Expand

$$8b^{6}a^{8}\left(cd\right)^{7}$$

Solution Steps

Expand \left(-2a^{2}bc^{2}d\right)^{3}.

$$\left(-\left(-2\right)^{3}\left(a^{2}\right)^{3}b^{3}\left(c^{2}\right)^{3}d^{3}\right)a^{2}b^{3}cd^{4}$$

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

$$\left(-\left(-2\right)^{3}a^{6}b^{3}\left(c^{2}\right)^{3}d^{3}\right)a^{2}b^{3}cd^{4}$$

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

$$\left(-\left(-2\right)^{3}a^{6}b^{3}c^{6}d^{3}\right)a^{2}b^{3}cd^{4}$$

Calculate -2 to the power of 3 and get -8.

$$\left(-\left(-8a^{6}b^{3}c^{6}d^{3}\right)\right)a^{2}b^{3}cd^{4}$$

The opposite of -8a^{6}b^{3}c^{6}d^{3} is 8a^{6}b^{3}c^{6}d^{3}.

$$8a^{6}b^{3}c^{6}d^{3}a^{2}b^{3}cd^{4}$$

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

$$8a^{8}b^{3}c^{6}d^{3}b^{3}cd^{4}$$

To multiply powers of the same base, add their exponents. Add 3 and 3 to get 6.

$$8a^{8}b^{6}c^{6}d^{3}cd^{4}$$

To multiply powers of the same base, add their exponents. Add 6 and 1 to get 7.

$$8a^{8}b^{6}c^{7}d^{3}d^{4}$$

To multiply powers of the same base, add their exponents. Add 3 and 4 to get 7.

$$8a^{8}b^{6}c^{7}d^{7}$$