Solve [(a^{3}b^5c^3)^4]^3

$$[ ( a ^ { 3 } b ^ { 5 } c ^ { 3 } ) ^ { 4 } ] ^ { 3 }$$

Evaluate

$$b^{60}\left(ac\right)^{36}$$

Solution Steps

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

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

To raise a power to another power, multiply the exponents. Multiply 3 and 4 to get 12.

$$\left(a^{12}\left(b^{5}\right)^{4}\left(c^{3}\right)^{4}\right)^{3}$$

To raise a power to another power, multiply the exponents. Multiply 5 and 4 to get 20.

$$\left(a^{12}b^{20}\left(c^{3}\right)^{4}\right)^{3}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 4 to get 12.

$$\left(a^{12}b^{20}c^{12}\right)^{3}$$

Expand \left(a^{12}b^{20}c^{12}\right)^{3}.

$$\left(a^{12}\right)^{3}\left(b^{20}\right)^{3}\left(c^{12}\right)^{3}$$

To raise a power to another power, multiply the exponents. Multiply 12 and 3 to get 36.

$$a^{36}\left(b^{20}\right)^{3}\left(c^{12}\right)^{3}$$

To raise a power to another power, multiply the exponents. Multiply 20 and 3 to get 60.

$$a^{36}b^{60}\left(c^{12}\right)^{3}$$

To raise a power to another power, multiply the exponents. Multiply 12 and 3 to get 36.

$$a^{36}b^{60}c^{36}$$

Expand

$$b^{60}\left(ac\right)^{36}$$

Solution Steps

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

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

To raise a power to another power, multiply the exponents. Multiply 3 and 4 to get 12.

$$\left(a^{12}\left(b^{5}\right)^{4}\left(c^{3}\right)^{4}\right)^{3}$$

To raise a power to another power, multiply the exponents. Multiply 5 and 4 to get 20.

$$\left(a^{12}b^{20}\left(c^{3}\right)^{4}\right)^{3}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 4 to get 12.

$$\left(a^{12}b^{20}c^{12}\right)^{3}$$

Expand \left(a^{12}b^{20}c^{12}\right)^{3}.

$$\left(a^{12}\right)^{3}\left(b^{20}\right)^{3}\left(c^{12}\right)^{3}$$

To raise a power to another power, multiply the exponents. Multiply 12 and 3 to get 36.

$$a^{36}\left(b^{20}\right)^{3}\left(c^{12}\right)^{3}$$

To raise a power to another power, multiply the exponents. Multiply 20 and 3 to get 60.

$$a^{36}b^{60}\left(c^{12}\right)^{3}$$

To raise a power to another power, multiply the exponents. Multiply 12 and 3 to get 36.

$$a^{36}b^{60}c^{36}$$