Solve frac{7(m^{5})^{6}+11(m^3)^10}{(3m^15)^2}

$$\frac { 7 ( m ^ { 5 } ) ^ { 6 } + 11 ( m ^ { 3 } ) ^ { 10 } } { ( 3 m ^ { 15 } ) ^ { 2 } }$$

Evaluate

$$2$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 5 and 6 to get 30.

$$\frac{7m^{30}+11\left(m^{3}\right)^{10}}{\left(3m^{15}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 10 to get 30.

$$\frac{7m^{30}+11m^{30}}{\left(3m^{15}\right)^{2}}$$

Combine 7m^{30} and 11m^{30} to get 18m^{30}.

$$\frac{18m^{30}}{\left(3m^{15}\right)^{2}}$$

Expand \left(3m^{15}\right)^{2}.

$$\frac{18m^{30}}{3^{2}\left(m^{15}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 15 and 2 to get 30.

$$\frac{18m^{30}}{3^{2}m^{30}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{18m^{30}}{9m^{30}}$$

Cancel out 9m^{30} in both numerator and denominator.

$$2$$

Factor

$$2$$