Solve (3a^2b^2c)(abc^2)^2

$$( 3 a ^ { 2 } b ^ { 2 } c ) ( a b c ^ { 2 } ) ^ { 2 }$$

Evaluate

$$3c^{5}\left(ab\right)^{4}$$

Solution Steps

Expand \left(abc^{2}\right)^{2}.

$$3a^{2}b^{2}ca^{2}b^{2}\left(c^{2}\right)^{2}$$

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

$$3a^{2}b^{2}ca^{2}b^{2}c^{4}$$

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

$$3a^{4}b^{2}cb^{2}c^{4}$$

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

$$3a^{4}b^{4}cc^{4}$$

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

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

Expand

$$3c^{5}\left(ab\right)^{4}$$

Solution Steps

Expand \left(abc^{2}\right)^{2}.

$$3a^{2}b^{2}ca^{2}b^{2}\left(c^{2}\right)^{2}$$

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

$$3a^{2}b^{2}ca^{2}b^{2}c^{4}$$

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

$$3a^{4}b^{2}cb^{2}c^{4}$$

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

$$3a^{4}b^{4}cc^{4}$$

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

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