Solve 6ab^2c*(2a^2bc)^2

$$6 a b ^ { 2 } c \cdot ( 2 a ^ { 2 } b c ) ^ { 2 }$$

Evaluate

$$24c^{3}b^{4}a^{5}$$

Solution Steps

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

$$6ab^{2}c\times 2^{2}\left(a^{2}\right)^{2}b^{2}c^{2}$$

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

$$6ab^{2}c\times 2^{2}a^{4}b^{2}c^{2}$$

Calculate 2 to the power of 2 and get 4.

$$6ab^{2}c\times 4a^{4}b^{2}c^{2}$$

Multiply 6 and 4 to get 24.

$$24ab^{2}ca^{4}b^{2}c^{2}$$

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

$$24a^{5}b^{2}cb^{2}c^{2}$$

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

$$24a^{5}b^{4}cc^{2}$$

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

$$24a^{5}b^{4}c^{3}$$

Expand

$$24c^{3}b^{4}a^{5}$$

Solution Steps

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

$$6ab^{2}c\times 2^{2}\left(a^{2}\right)^{2}b^{2}c^{2}$$

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

$$6ab^{2}c\times 2^{2}a^{4}b^{2}c^{2}$$

Calculate 2 to the power of 2 and get 4.

$$6ab^{2}c\times 4a^{4}b^{2}c^{2}$$

Multiply 6 and 4 to get 24.

$$24ab^{2}ca^{4}b^{2}c^{2}$$

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

$$24a^{5}b^{2}cb^{2}c^{2}$$

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

$$24a^{5}b^{4}cc^{2}$$

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

$$24a^{5}b^{4}c^{3}$$