Solve frac{(2^frac{3{5}}*5^frac{2{3}})^15}{10^9}

$$\frac { ( 2 ^ { \frac { 3 } { 5 } } \cdot 5 ^ { \frac { 2 } { 3 } } ) ^ { 15 } } { 10 ^ { 9 } }$$

Evaluate

$$5$$

Solution Steps

Expand \left(2^{\frac{3}{5}}\times 5^{\frac{2}{3}}\right)^{15}.

$$\frac{\left(2^{\frac{3}{5}}\right)^{15}\times \left(5^{\frac{2}{3}}\right)^{15}}{10^{9}}$$

To raise a power to another power, multiply the exponents. Multiply \frac{3}{5} and 15 to get 9.

$$\frac{2^{9}\times \left(5^{\frac{2}{3}}\right)^{15}}{10^{9}}$$

To raise a power to another power, multiply the exponents. Multiply \frac{2}{3} and 15 to get 10.

$$\frac{2^{9}\times 5^{10}}{10^{9}}$$

Calculate 2 to the power of 9 and get 512.

$$\frac{512\times 5^{10}}{10^{9}}$$

Calculate 5 to the power of 10 and get 9765625.

$$\frac{512\times 9765625}{10^{9}}$$

Multiply 512 and 9765625 to get 5000000000.

$$\frac{5000000000}{10^{9}}$$

Calculate 10 to the power of 9 and get 1000000000.

$$\frac{5000000000}{1000000000}$$

Divide 5000000000 by 1000000000 to get 5.

$$5$$

Factor

$$5$$