Solve {l}{4^{2}*3^{3}*4^{2}}{4^5*3^3*3^3*4^4}

$$\left. \begin{array} { l } { 4 ^ { 2 } \times 3 ^ { 3 } \times 4 ^ { 2 } } \\ { 4 ^ { 5 } \times 3 ^ { 3 } \times 3 ^ { 3 } \times 4 ^ { 4 } } \end{array} \right.$$

Sort

$$6912,\ 191102976$$

Solution Steps

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

$$sort(4^{4}\times 3^{3},4^{5}\times 3^{3}\times 3^{3}\times 4^{4})$$

To multiply powers of the same base, add their exponents. Add 5 and 4 to get 9.

$$sort(4^{4}\times 3^{3},4^{9}\times 3^{3}\times 3^{3})$$

To multiply powers of the same base, add their exponents. Add 3 and 3 to get 6.

$$sort(4^{4}\times 3^{3},4^{9}\times 3^{6})$$

Calculate 4 to the power of 4 and get 256.

$$sort(256\times 3^{3},4^{9}\times 3^{6})$$

Calculate 3 to the power of 3 and get 27.

$$sort(256\times 27,4^{9}\times 3^{6})$$

Multiply 256 and 27 to get 6912.

$$sort(6912,4^{9}\times 3^{6})$$

Calculate 4 to the power of 9 and get 262144.

$$sort(6912,262144\times 3^{6})$$

Calculate 3 to the power of 6 and get 729.

$$sort(6912,262144\times 729)$$

Multiply 262144 and 729 to get 191102976.

$$sort(6912,191102976)$$

The list values are already in order.

$$6912,191102976$$

Evaluate

$$6912,\ 191102976$$