Solve (7^{9})^2:(7^4*7^2)^2

$$( 7 ^ { 9 } ) ^ { 2 } : ( 7 ^ { 4 } \cdot 7 ^ { 2 } ) ^ { 2 }$$

Evaluate

$$117649$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 9 and 2 to get 18.

$$\frac{7^{18}}{\left(7^{4}\times 7^{2}\right)^{2}}$$

To multiply powers of the same base, add their exponents. Add 4 and 2 to get 6.

$$\frac{7^{18}}{\left(7^{6}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 6 and 2 to get 12.

$$\frac{7^{18}}{7^{12}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 12 from 18 to get 6.

$$7^{6}$$

Calculate 7 to the power of 6 and get 117649.

$$117649$$

Factor

$$7^{6}$$