Solve [(7^{3}*7^{4})^{3}:[(7^3)^4*(7^4)^2]]

$$[ ( 7 ^ { 3 } \cdot 7 ^ { 4 } ) ^ { 3 } : [ ( 7 ^ { 3 } ) ^ { 4 } \cdot ( 7 ^ { 4 } ) ^ { 2 } ] ]$$

Evaluate

$$7$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and 4 to get 7.

$$\frac{\left(7^{7}\right)^{3}}{\left(7^{3}\right)^{4}\times \left(7^{4}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 7 and 3 to get 21.

$$\frac{7^{21}}{\left(7^{3}\right)^{4}\times \left(7^{4}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 4 to get 12.

$$\frac{7^{21}}{7^{12}\times \left(7^{4}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 2 to get 8.

$$\frac{7^{21}}{7^{12}\times 7^{8}}$$

To multiply powers of the same base, add their exponents. Add 12 and 8 to get 20.

$$\frac{7^{21}}{7^{20}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 20 from 21 to get 1.

$$7^{1}$$

Calculate 7 to the power of 1 and get 7.

$$7$$

Factor

$$7$$