Solve {l}{x=4}{y={(x^3)}^13*4x^13}{text{Solvefor}ztext{where}}{z=y}

$$\left. \begin{array} { l } { x = 4 }\\ { y = {(x ^ {3})} ^ {13} \cdot 4 x ^ {13} }\\ { \text{Solve for } z \text{ where} } \\ { z = y } \end{array} \right.$$

Solve for x, y, z

$$z=81129638414606681695789005144064$$

Solution Steps

Consider the second equation. Insert the known values of variables into the equation.

$$y=\left(4^{3}\right)^{13}\times 4\times 4^{13}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 13 to get 39.

$$y=4^{39}\times 4\times 4^{13}$$

To multiply powers of the same base, add their exponents. Add 39 and 1 to get 40.

$$y=4^{40}\times 4^{13}$$

To multiply powers of the same base, add their exponents. Add 40 and 13 to get 53.

$$y=4^{53}$$

Calculate 4 to the power of 53 and get 81129638414606681695789005144064.

$$y=81129638414606681695789005144064$$

Consider the third equation. Insert the known values of variables into the equation.

$$z=81129638414606681695789005144064$$

The system is now solved.

$$x=4 y=81129638414606681695789005144064 z=81129638414606681695789005144064$$