Solve (5^{3})^{2}:(5^{2})^{3}+(6^7:6^3):(6^2*6^2)

$$( 5 ^ { 3 } ) ^ { 2 } : ( 5 ^ { 2 } ) ^ { 3 } + ( 6 ^ { 7 } : 6 ^ { 3 } ) : ( 6 ^ { 2 } \cdot 6 ^ { 2 } )$$

Evaluate

$$2$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

$$\frac{5^{6}}{\left(5^{2}\right)^{3}}+\frac{\frac{6^{7}}{6^{3}}}{6^{2}\times 6^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.

$$\frac{5^{6}}{5^{6}}+\frac{\frac{6^{7}}{6^{3}}}{6^{2}\times 6^{2}}$$

Divide 5^{6} by 5^{6} to get 1.

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

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 3 from 7 to get 4.

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

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

$$1+\frac{6^{4}}{6^{4}}$$

Divide 6^{4} by 6^{4} to get 1.

$$1+1$$

Add 1 and 1 to get 2.

$$2$$

Factor

$$2$$