Solve {[(3*Z^2)^5]^3}^6

$$\{ [ ( 3 * Z ^ { 2 } ) ^ { 5 } ] ^ { 3 } \} ^ { 6 }$$

Evaluate

$$8727963568087712425891397479476727340041449Z^{180}$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 5 and 3 to get 15.

$$\left(\left(3Z^{2}\right)^{15}\right)^{6}$$

Expand \left(3Z^{2}\right)^{15}.

$$\left(3^{15}\left(Z^{2}\right)^{15}\right)^{6}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 15 to get 30.

$$\left(3^{15}Z^{30}\right)^{6}$$

Calculate 3 to the power of 15 and get 14348907.

$$\left(14348907Z^{30}\right)^{6}$$

Expand \left(14348907Z^{30}\right)^{6}.

$$14348907^{6}\left(Z^{30}\right)^{6}$$

To raise a power to another power, multiply the exponents. Multiply 30 and 6 to get 180.

$$14348907^{6}Z^{180}$$

Calculate 14348907 to the power of 6 and get 8727963568087712425891397479476727340041449.

$$8727963568087712425891397479476727340041449Z^{180}$$

Expand

$$8727963568087712425891397479476727340041449Z^{180}$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 5 and 3 to get 15.

$$\left(\left(3Z^{2}\right)^{15}\right)^{6}$$

Expand \left(3Z^{2}\right)^{15}.

$$\left(3^{15}\left(Z^{2}\right)^{15}\right)^{6}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 15 to get 30.

$$\left(3^{15}Z^{30}\right)^{6}$$

Calculate 3 to the power of 15 and get 14348907.

$$\left(14348907Z^{30}\right)^{6}$$

Expand \left(14348907Z^{30}\right)^{6}.

$$14348907^{6}\left(Z^{30}\right)^{6}$$

To raise a power to another power, multiply the exponents. Multiply 30 and 6 to get 180.

$$14348907^{6}Z^{180}$$

Calculate 14348907 to the power of 6 and get 8727963568087712425891397479476727340041449.

$$8727963568087712425891397479476727340041449Z^{180}$$