Solve (2a^{2}bc^2)(3ab^3c^2)^3(3a)

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

Evaluate

$$162a^{6}c^{8}b^{10}$$

Solution Steps

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

$$2a^{3}bc^{2}\times \left(3ab^{3}c^{2}\right)^{3}\times 3$$

Expand \left(3ab^{3}c^{2}\right)^{3}.

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

To raise a power to another power, multiply the exponents. Multiply 3 and 3 to get 9.

$$2a^{3}bc^{2}\times 3^{3}a^{3}b^{9}\left(c^{2}\right)^{3}\times 3$$

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

$$2a^{3}bc^{2}\times 3^{3}a^{3}b^{9}c^{6}\times 3$$

Calculate 3 to the power of 3 and get 27.

$$2a^{3}bc^{2}\times 27a^{3}b^{9}c^{6}\times 3$$

Multiply 2 and 27 to get 54.

$$54a^{3}bc^{2}a^{3}b^{9}c^{6}\times 3$$

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

$$54a^{6}bc^{2}b^{9}c^{6}\times 3$$

To multiply powers of the same base, add their exponents. Add 1 and 9 to get 10.

$$54a^{6}b^{10}c^{2}c^{6}\times 3$$

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

$$54a^{6}b^{10}c^{8}\times 3$$

Multiply 54 and 3 to get 162.

$$162a^{6}b^{10}c^{8}$$

Expand

$$162a^{6}c^{8}b^{10}$$

Solution Steps

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

$$2a^{3}bc^{2}\times \left(3ab^{3}c^{2}\right)^{3}\times 3$$

Expand \left(3ab^{3}c^{2}\right)^{3}.

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

To raise a power to another power, multiply the exponents. Multiply 3 and 3 to get 9.

$$2a^{3}bc^{2}\times 3^{3}a^{3}b^{9}\left(c^{2}\right)^{3}\times 3$$

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

$$2a^{3}bc^{2}\times 3^{3}a^{3}b^{9}c^{6}\times 3$$

Calculate 3 to the power of 3 and get 27.

$$2a^{3}bc^{2}\times 27a^{3}b^{9}c^{6}\times 3$$

Multiply 2 and 27 to get 54.

$$54a^{3}bc^{2}a^{3}b^{9}c^{6}\times 3$$

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

$$54a^{6}bc^{2}b^{9}c^{6}\times 3$$

To multiply powers of the same base, add their exponents. Add 1 and 9 to get 10.

$$54a^{6}b^{10}c^{2}c^{6}\times 3$$

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

$$54a^{6}b^{10}c^{8}\times 3$$

Multiply 54 and 3 to get 162.

$$162a^{6}b^{10}c^{8}$$