Solve {l}{1^{circ}2^{3}*3^{2}*7*2^{2}*3}{2^{circ}3^{5}*5^2*7^2*3^2*5^2*13}

$$\left. \begin{array} { l } { 1 ^ { \circ } 2 ^ { 3 } \times 3 ^ { 2 } \times 7 \times 2 ^ { 2 } \times 3 } \\ { 2 ^ { \circ } 3 ^ { 5 } \times 5 ^ { 2 } \times 7 ^ { 2 } \times 3 ^ { 2 } \times 5 ^ { 2 } \times 13 } \end{array} \right.$$

Sort

$$6048,\ 1741398750$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and 2 to get 5.

$$sort(1\times 2^{5}\times 3^{2}\times 7\times 3,2\times 3^{5}\times 5^{2}\times 7^{2}\times 3^{2}\times 5^{2}\times 13)$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$sort(1\times 2^{5}\times 3^{3}\times 7,2\times 3^{5}\times 5^{2}\times 7^{2}\times 3^{2}\times 5^{2}\times 13)$$

To multiply powers of the same base, add their exponents. Add 5 and 2 to get 7.

$$sort(1\times 2^{5}\times 3^{3}\times 7,2\times 3^{7}\times 5^{2}\times 7^{2}\times 5^{2}\times 13)$$

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

$$sort(1\times 2^{5}\times 3^{3}\times 7,2\times 3^{7}\times 5^{4}\times 7^{2}\times 13)$$

Calculate 2 to the power of 5 and get 32.

$$sort(1\times 32\times 3^{3}\times 7,2\times 3^{7}\times 5^{4}\times 7^{2}\times 13)$$

Multiply 1 and 32 to get 32.

$$sort(32\times 3^{3}\times 7,2\times 3^{7}\times 5^{4}\times 7^{2}\times 13)$$

Calculate 3 to the power of 3 and get 27.

$$sort(32\times 27\times 7,2\times 3^{7}\times 5^{4}\times 7^{2}\times 13)$$

Multiply 32 and 27 to get 864.

$$sort(864\times 7,2\times 3^{7}\times 5^{4}\times 7^{2}\times 13)$$

Multiply 864 and 7 to get 6048.

$$sort(6048,2\times 3^{7}\times 5^{4}\times 7^{2}\times 13)$$

Calculate 3 to the power of 7 and get 2187.

$$sort(6048,2\times 2187\times 5^{4}\times 7^{2}\times 13)$$

Multiply 2 and 2187 to get 4374.

$$sort(6048,4374\times 5^{4}\times 7^{2}\times 13)$$

Calculate 5 to the power of 4 and get 625.

$$sort(6048,4374\times 625\times 7^{2}\times 13)$$

Multiply 4374 and 625 to get 2733750.

$$sort(6048,2733750\times 7^{2}\times 13)$$

Calculate 7 to the power of 2 and get 49.

$$sort(6048,2733750\times 49\times 13)$$

Multiply 2733750 and 49 to get 133953750.

$$sort(6048,133953750\times 13)$$

Multiply 133953750 and 13 to get 1741398750.

$$sort(6048,1741398750)$$

The list values are already in order.

$$6048,1741398750$$

Evaluate

$$6048,\ 1741398750$$