Solve frac{7^{2}*2^{3}*7^{1}*2^{2}*7^{3}*2^{1}*7^{0}}{7^{2}*2^0*7^2*2^2*2^1}

$$\frac { 7 ^ { 2 } \times 2 ^ { 3 } \times 7 ^ { 1 } \times 2 ^ { 2 } \times 7 ^ { 3 } \times 2 ^ { 1 } \times 7 ^ { 0 } } { 7 ^ { 2 } \times 2 ^ { 0 } \times 7 ^ { 2 } \times 2 ^ { 2 } \times 2 ^ { 1 } }$$

Evaluate

$$392$$

Solution Steps

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

$$\frac{7^{3}\times 2^{3}\times 2^{2}\times 7^{3}\times 2^{1}\times 7^{0}}{7^{2}\times 2^{0}\times 7^{2}\times 2^{2}\times 2^{1}}$$

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

$$\frac{7^{6}\times 2^{3}\times 2^{2}\times 2^{1}\times 7^{0}}{7^{2}\times 2^{0}\times 7^{2}\times 2^{2}\times 2^{1}}$$

To multiply powers of the same base, add their exponents. Add 6 and 0 to get 6.

$$\frac{7^{6}\times 2^{3}\times 2^{2}\times 2^{1}}{7^{2}\times 2^{0}\times 7^{2}\times 2^{2}\times 2^{1}}$$

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

$$\frac{7^{6}\times 2^{5}\times 2^{1}}{7^{2}\times 2^{0}\times 7^{2}\times 2^{2}\times 2^{1}}$$

To multiply powers of the same base, add their exponents. Add 5 and 1 to get 6.

$$\frac{7^{6}\times 2^{6}}{7^{2}\times 2^{0}\times 7^{2}\times 2^{2}\times 2^{1}}$$

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

$$\frac{7^{6}\times 2^{6}}{7^{4}\times 2^{0}\times 2^{2}\times 2^{1}}$$

To multiply powers of the same base, add their exponents. Add 0 and 2 to get 2.

$$\frac{7^{6}\times 2^{6}}{7^{4}\times 2^{2}\times 2^{1}}$$

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

$$\frac{7^{6}\times 2^{6}}{7^{4}\times 2^{3}}$$

Cancel out 2^{3}\times 7^{4} in both numerator and denominator.

$$2^{3}\times 7^{2}$$

Calculate 2 to the power of 3 and get 8.

$$8\times 7^{2}$$

Calculate 7 to the power of 2 and get 49.

$$8\times 49$$

Multiply 8 and 49 to get 392.

$$392$$

Factor

$$2^{3}\times 7^{2}$$