Solve frac{(5^frac{3{5}}*11^frac{7{11}})^55}{55^33}

$$\frac { ( 5 ^ { \frac { 3 } { 5 } } \cdot 11 ^ { \frac { 7 } { 11 } } ) ^ { 55 } } { 55 ^ { 33 } }$$

Evaluate

$$121$$

Solution Steps

Expand \left(5^{\frac{3}{5}}\times 11^{\frac{7}{11}}\right)^{55}.

$$\frac{\left(5^{\frac{3}{5}}\right)^{55}\times \left(11^{\frac{7}{11}}\right)^{55}}{55^{33}}$$

To raise a power to another power, multiply the exponents. Multiply \frac{3}{5} and 55 to get 33.

$$\frac{5^{33}\times \left(11^{\frac{7}{11}}\right)^{55}}{55^{33}}$$

To raise a power to another power, multiply the exponents. Multiply \frac{7}{11} and 55 to get 35.

$$\frac{5^{33}\times 11^{35}}{55^{33}}$$

Calculate 5 to the power of 33 and get 116415321826934814453125.

$$\frac{116415321826934814453125\times 11^{35}}{55^{33}}$$

Calculate 11 to the power of 35 and get 2810243684806424785061213903353404851.

$$\frac{116415321826934814453125\times 2810243684806424785061213903353404851}{55^{33}}$$

Multiply 116415321826934814453125 and 2810243684806424785061213903353404851 to get 327155422978851104278724396526045730686746537685394287109375.

$$\frac{327155422978851104278724396526045730686746537685394287109375}{55^{33}}$$

Calculate 55 to the power of 33 and get 2703763826271496729576234682033435790799558162689208984375.

$$\frac{327155422978851104278724396526045730686746537685394287109375}{2703763826271496729576234682033435790799558162689208984375}$$

Divide 327155422978851104278724396526045730686746537685394287109375 by 2703763826271496729576234682033435790799558162689208984375 to get 121.

$$121$$

Factor

$$11^{2}$$