Solve [(a^{2}b^{2}c^{4})(ab^2c^1)(c^0)]^2

$$[ ( a ^ { 2 } b ^ { 2 } c ^ { 4 } ) ( a b ^ { 2 } c ^ { 1 } ) ( c ^ { 0 } ) ] ^ { 2 }$$

Evaluate

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

Solution Steps

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

$$\left(a^{3}b^{2}c^{4}b^{2}c^{1}c^{0}\right)^{2}$$

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

$$\left(a^{3}b^{4}c^{4}c^{1}c^{0}\right)^{2}$$

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

$$\left(a^{3}b^{4}c^{5}c^{0}\right)^{2}$$

To multiply powers of the same base, add their exponents. Add 5 and 0 to get 5.

$$\left(a^{3}b^{4}c^{5}\right)^{2}$$

Expand \left(a^{3}b^{4}c^{5}\right)^{2}.

$$\left(a^{3}\right)^{2}\left(b^{4}\right)^{2}\left(c^{5}\right)^{2}$$

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

$$a^{6}\left(b^{4}\right)^{2}\left(c^{5}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 2 to get 8.

$$a^{6}b^{8}\left(c^{5}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 5 and 2 to get 10.

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

Expand

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

Solution Steps

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

$$\left(a^{3}b^{2}c^{4}b^{2}c^{1}c^{0}\right)^{2}$$

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

$$\left(a^{3}b^{4}c^{4}c^{1}c^{0}\right)^{2}$$

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

$$\left(a^{3}b^{4}c^{5}c^{0}\right)^{2}$$

To multiply powers of the same base, add their exponents. Add 5 and 0 to get 5.

$$\left(a^{3}b^{4}c^{5}\right)^{2}$$

Expand \left(a^{3}b^{4}c^{5}\right)^{2}.

$$\left(a^{3}\right)^{2}\left(b^{4}\right)^{2}\left(c^{5}\right)^{2}$$

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

$$a^{6}\left(b^{4}\right)^{2}\left(c^{5}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 2 to get 8.

$$a^{6}b^{8}\left(c^{5}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 5 and 2 to get 10.

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