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

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

Evaluate

$$10$$

Solution Steps

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

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

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

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

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

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

Calculate 2 to the power of 10 and get 1024.

$$\frac{1024\times 5^{10}}{10^{9}}$$

Calculate 5 to the power of 10 and get 9765625.

$$\frac{1024\times 9765625}{10^{9}}$$

Multiply 1024 and 9765625 to get 10000000000.

$$\frac{10000000000}{10^{9}}$$

Calculate 10 to the power of 9 and get 1000000000.

$$\frac{10000000000}{1000000000}$$

Divide 10000000000 by 1000000000 to get 10.

$$10$$

Factor

$$2\times 5$$