Solve (5b^{3}c^2)*4(b^2c^3)^2=

$$( 5 b ^ { 3 } c ^ { 2 } ) \times 4 ( b ^ { 2 } c ^ { 3 } ) ^ { 2 } =$$

Evaluate

$$20b^{7}c^{8}$$

Solution Steps

Multiply 5 and 4 to get 20.

$$20b^{3}c^{2}\left(b^{2}c^{3}\right)^{2}$$

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

$$20b^{3}c^{2}\left(b^{2}\right)^{2}\left(c^{3}\right)^{2}$$

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

$$20b^{3}c^{2}b^{4}\left(c^{3}\right)^{2}$$

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

$$20b^{3}c^{2}b^{4}c^{6}$$

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

$$20b^{7}c^{2}c^{6}$$

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

$$20b^{7}c^{8}$$

Expand

$$20b^{7}c^{8}$$

Solution Steps

Multiply 5 and 4 to get 20.

$$20b^{3}c^{2}\left(b^{2}c^{3}\right)^{2}$$

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

$$20b^{3}c^{2}\left(b^{2}\right)^{2}\left(c^{3}\right)^{2}$$

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

$$20b^{3}c^{2}b^{4}\left(c^{3}\right)^{2}$$

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

$$20b^{3}c^{2}b^{4}c^{6}$$

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

$$20b^{7}c^{2}c^{6}$$

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

$$20b^{7}c^{8}$$