Solve frac{3^{5}*3^{2}+3^{4}(3^{10}div3^{8})}{3^5*3^4div(3^2*3^3)}

$$\frac { 3 ^ { 5 } \times 3 ^ { 2 } + 3 ^ { 4 } ( 3 ^ { 10 } \div 3 ^ { 8 } ) } { 3 ^ { 5 } \times 3 ^ { 4 } \div ( 3 ^ { 2 } \times 3 ^ { 3 } ) }$$

Evaluate

$$36$$

Solution Steps

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

$$\frac{3^{7}+3^{4}\times \frac{3^{10}}{3^{8}}}{\frac{3^{5}\times 3^{4}}{3^{2}\times 3^{3}}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 8 from 10 to get 2.

$$\frac{3^{7}+3^{4}\times 3^{2}}{\frac{3^{5}\times 3^{4}}{3^{2}\times 3^{3}}}$$

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

$$\frac{3^{7}+3^{6}}{\frac{3^{5}\times 3^{4}}{3^{2}\times 3^{3}}}$$

To multiply powers of the same base, add their exponents. Add 5 and 4 to get 9.

$$\frac{3^{7}+3^{6}}{\frac{3^{9}}{3^{2}\times 3^{3}}}$$

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

$$\frac{3^{7}+3^{6}}{\frac{3^{9}}{3^{5}}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 5 from 9 to get 4.

$$\frac{3^{7}+3^{6}}{3^{4}}$$

Calculate 3 to the power of 7 and get 2187.

$$\frac{2187+3^{6}}{3^{4}}$$

Calculate 3 to the power of 6 and get 729.

$$\frac{2187+729}{3^{4}}$$

Add 2187 and 729 to get 2916.

$$\frac{2916}{3^{4}}$$

Calculate 3 to the power of 4 and get 81.

$$\frac{2916}{81}$$

Divide 2916 by 81 to get 36.

$$36$$

Factor

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