Solve sqrt[4]{5.13*10^25*729/5.7*10^-8*10^20}

$$\sqrt[ 4 ]{ \frac{ 5.13 \cdot { 10 }^{ 25 } \times 729 }{ 5.7 \cdot { 10 }^{ -8 } \times { 10 }^{ 20 } } }$$

Evaluate

$$9000$$

Solution Steps

To multiply powers of the same base, add their exponents. Add -8 and 20 to get 12.

$$\sqrt[4]{\frac{5.13\times 10^{25}\times 729}{5.7\times 10^{12}}}$$

Cancel out 10^{12} in both numerator and denominator.

$$\sqrt[4]{\frac{5.13\times 729\times 10^{13}}{5.7}}$$

Multiply 5.13 and 729 to get 3739.77.

$$\sqrt[4]{\frac{3739.77\times 10^{13}}{5.7}}$$

Calculate 10 to the power of 13 and get 10000000000000.

$$\sqrt[4]{\frac{3739.77\times 10000000000000}{5.7}}$$

Multiply 3739.77 and 10000000000000 to get 37397700000000000.

$$\sqrt[4]{\frac{37397700000000000}{5.7}}$$

Expand \frac{37397700000000000}{5.7} by multiplying both numerator and the denominator by 10.

$$\sqrt[4]{\frac{373977000000000000}{57}}$$

Divide 373977000000000000 by 57 to get 6561000000000000.

$$\sqrt[4]{6561000000000000}$$

Calculate \sqrt[4]{6561000000000000} and get 9000.

$$9000$$

Factor

$$2^{3}\times 3^{2}\times 5^{3}$$