Solve sqrt[3]{sqrt{5^8*5*5^9}}

$$\sqrt[ 3 ]{ \sqrt{ { 5 }^{ 8 } \times 5 \times { 5 }^{ 9 } } }$$

Evaluate

$$125$$

Solution Steps

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

$$\sqrt[3]{\sqrt{5^{9}\times 5^{9}}}$$

To multiply powers of the same base, add their exponents. Add 9 and 9 to get 18.

$$\sqrt[3]{\sqrt{5^{18}}}$$

Calculate 5 to the power of 18 and get 3814697265625.

$$\sqrt[3]{\sqrt{3814697265625}}$$

Calculate the square root of 3814697265625 and get 1953125.

$$\sqrt[3]{1953125}$$

Calculate \sqrt[3]{1953125} and get 125.

$$125$$

Factor

$$5^{3}$$