Solve {left(left(a^3b^5c^7right)^4right)}^-3

$${ \left( { \left( { a }^{ 3 } { b }^{ 5 } { c }^{ 7 } \right) }^{ 4 } \right) }^{ -3 }$$

Evaluate

$$\frac{1}{a^{36}b^{60}c^{84}}$$

Solution Steps

Expand \left(a^{3}b^{5}c^{7}\right)^{4}.

$$\left(\left(a^{3}\right)^{4}\left(b^{5}\right)^{4}\left(c^{7}\right)^{4}\right)^{-3}$$

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

$$\left(a^{12}\left(b^{5}\right)^{4}\left(c^{7}\right)^{4}\right)^{-3}$$

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

$$\left(a^{12}b^{20}\left(c^{7}\right)^{4}\right)^{-3}$$

To raise a power to another power, multiply the exponents. Multiply 7 and 4 to get 28.

$$\left(a^{12}b^{20}c^{28}\right)^{-3}$$

Expand \left(a^{12}b^{20}c^{28}\right)^{-3}.

$$\left(a^{12}\right)^{-3}\left(b^{20}\right)^{-3}\left(c^{28}\right)^{-3}$$

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

$$a^{-36}\left(b^{20}\right)^{-3}\left(c^{28}\right)^{-3}$$

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

$$a^{-36}b^{-60}\left(c^{28}\right)^{-3}$$

To raise a power to another power, multiply the exponents. Multiply 28 and -3 to get -84.

$$a^{-36}b^{-60}c^{-84}$$

Expand

$$\frac{1}{a^{36}b^{60}c^{84}}$$

Solution Steps

Expand \left(a^{3}b^{5}c^{7}\right)^{4}.

$$\left(\left(a^{3}\right)^{4}\left(b^{5}\right)^{4}\left(c^{7}\right)^{4}\right)^{-3}$$

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

$$\left(a^{12}\left(b^{5}\right)^{4}\left(c^{7}\right)^{4}\right)^{-3}$$

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

$$\left(a^{12}b^{20}\left(c^{7}\right)^{4}\right)^{-3}$$

To raise a power to another power, multiply the exponents. Multiply 7 and 4 to get 28.

$$\left(a^{12}b^{20}c^{28}\right)^{-3}$$

Expand \left(a^{12}b^{20}c^{28}\right)^{-3}.

$$\left(a^{12}\right)^{-3}\left(b^{20}\right)^{-3}\left(c^{28}\right)^{-3}$$

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

$$a^{-36}\left(b^{20}\right)^{-3}\left(c^{28}\right)^{-3}$$

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

$$a^{-36}b^{-60}\left(c^{28}\right)^{-3}$$

To raise a power to another power, multiply the exponents. Multiply 28 and -3 to get -84.

$$a^{-36}b^{-60}c^{-84}$$