Solve frac{(5^{13})(5^2)(5^15)}{(5^8)(5)(5^19)}

$$\frac { ( 5 ^ { 13 } ) ( 5 ^ { 2 } ) ( 5 ^ { 15 } ) } { ( 5 ^ { 8 } ) ( 5 ) ( 5 ^ { 19 } ) }$$

Evaluate

$$25$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 13 and 2 to get 15.

$$\frac{5^{15}\times 5^{15}}{5^{8}\times 5\times 5^{19}}$$

To multiply powers of the same base, add their exponents. Add 15 and 15 to get 30.

$$\frac{5^{30}}{5^{8}\times 5\times 5^{19}}$$

To multiply powers of the same base, add their exponents. Add 8 and 1 to get 9.

$$\frac{5^{30}}{5^{9}\times 5^{19}}$$

To multiply powers of the same base, add their exponents. Add 9 and 19 to get 28.

$$\frac{5^{30}}{5^{28}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 28 from 30 to get 2.

$$5^{2}$$

Calculate 5 to the power of 2 and get 25.

$$25$$

Factor

$$5^{2}$$