Solve (-2ab)^4*3abc*(c^2d)^2*2bcd=

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

Evaluate

$$96d^{3}a^{5}\left(bc\right)^{6}$$

Solution Steps

Multiply b and b to get b^{2}.

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

Multiply c and c to get c^{2}.

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

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

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

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

$$16a^{4}b^{4}\times 3ab^{2}c^{2}\left(c^{2}d\right)^{2}\times 2d$$

Multiply 16 and 3 to get 48.

$$48a^{4}b^{4}ab^{2}c^{2}\left(c^{2}d\right)^{2}\times 2d$$

To multiply powers of the same base, add their exponents. Add 4 and 1 to get 5.

$$48a^{5}b^{4}b^{2}c^{2}\left(c^{2}d\right)^{2}\times 2d$$

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

$$48a^{5}b^{6}c^{2}\left(c^{2}d\right)^{2}\times 2d$$

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

$$48a^{5}b^{6}c^{2}\left(c^{2}\right)^{2}d^{2}\times 2d$$

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

$$48a^{5}b^{6}c^{2}c^{4}d^{2}\times 2d$$

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

$$48a^{5}b^{6}c^{6}d^{2}\times 2d$$

Multiply 48 and 2 to get 96.

$$96a^{5}b^{6}c^{6}d^{2}d$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$96a^{5}b^{6}c^{6}d^{3}$$

Expand

$$96d^{3}a^{5}\left(bc\right)^{6}$$

Solution Steps

Multiply b and b to get b^{2}.

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

Multiply c and c to get c^{2}.

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

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

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

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

$$16a^{4}b^{4}\times 3ab^{2}c^{2}\left(c^{2}d\right)^{2}\times 2d$$

Multiply 16 and 3 to get 48.

$$48a^{4}b^{4}ab^{2}c^{2}\left(c^{2}d\right)^{2}\times 2d$$

To multiply powers of the same base, add their exponents. Add 4 and 1 to get 5.

$$48a^{5}b^{4}b^{2}c^{2}\left(c^{2}d\right)^{2}\times 2d$$

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

$$48a^{5}b^{6}c^{2}\left(c^{2}d\right)^{2}\times 2d$$

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

$$48a^{5}b^{6}c^{2}\left(c^{2}\right)^{2}d^{2}\times 2d$$

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

$$48a^{5}b^{6}c^{2}c^{4}d^{2}\times 2d$$

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

$$48a^{5}b^{6}c^{6}d^{2}\times 2d$$

Multiply 48 and 2 to get 96.

$$96a^{5}b^{6}c^{6}d^{2}d$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$96a^{5}b^{6}c^{6}d^{3}$$