Solve n^2=2^9*5^3/10^5

$$n ^ { 2 } = \frac { 2 ^ { 9 } \cdot 5 ^ { 3 } } { 10 ^ { 5 } }$$

Solve for n

$$n=\frac{4}{5}=0.8$$

$$n=-\frac{4}{5}=-0.8$$

Steps Using Difference of Squares

Calculate 2 to the power of 9 and get 512.

$$n^{2}=\frac{512\times 5^{3}}{10^{5}}$$

Calculate 5 to the power of 3 and get 125.

$$n^{2}=\frac{512\times 125}{10^{5}}$$

Multiply 512 and 125 to get 64000.

$$n^{2}=\frac{64000}{10^{5}}$$

Calculate 10 to the power of 5 and get 100000.

$$n^{2}=\frac{64000}{100000}$$

Reduce the fraction \frac{64000}{100000} to lowest terms by extracting and canceling out 4000.

$$n^{2}=\frac{16}{25}$$

Subtract \frac{16}{25} from both sides.

$$n^{2}-\frac{16}{25}=0$$

Multiply both sides by 25.

$$25n^{2}-16=0$$

Consider 25n^{2}-16. Rewrite 25n^{2}-16 as \left(5n\right)^{2}-4^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(5n-4\right)\left(5n+4\right)=0$$

To find equation solutions, solve 5n-4=0 and 5n+4=0.

$$n=\frac{4}{5} n=-\frac{4}{5}$$

Steps by Finding Square Root

Calculate 2 to the power of 9 and get 512.

$$n^{2}=\frac{512\times 5^{3}}{10^{5}}$$

Calculate 5 to the power of 3 and get 125.

$$n^{2}=\frac{512\times 125}{10^{5}}$$

Multiply 512 and 125 to get 64000.

$$n^{2}=\frac{64000}{10^{5}}$$

Calculate 10 to the power of 5 and get 100000.

$$n^{2}=\frac{64000}{100000}$$

Reduce the fraction \frac{64000}{100000} to lowest terms by extracting and canceling out 4000.

$$n^{2}=\frac{16}{25}$$

Take the square root of both sides of the equation.

$$n=\frac{4}{5} n=-\frac{4}{5}$$

Steps Using the Quadratic Formula

Calculate 2 to the power of 9 and get 512.

$$n^{2}=\frac{512\times 5^{3}}{10^{5}}$$

Calculate 5 to the power of 3 and get 125.

$$n^{2}=\frac{512\times 125}{10^{5}}$$

Multiply 512 and 125 to get 64000.

$$n^{2}=\frac{64000}{10^{5}}$$

Calculate 10 to the power of 5 and get 100000.

$$n^{2}=\frac{64000}{100000}$$

Reduce the fraction \frac{64000}{100000} to lowest terms by extracting and canceling out 4000.

$$n^{2}=\frac{16}{25}$$

Subtract \frac{16}{25} from both sides.

$$n^{2}-\frac{16}{25}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -\frac{16}{25} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$n=\frac{0±\sqrt{0^{2}-4\left(-\frac{16}{25}\right)}}{2}$$

Square 0.

$$n=\frac{0±\sqrt{-4\left(-\frac{16}{25}\right)}}{2}$$

Multiply -4 times -\frac{16}{25}.

$$n=\frac{0±\sqrt{\frac{64}{25}}}{2}$$

Take the square root of \frac{64}{25}.

$$n=\frac{0±\frac{8}{5}}{2}$$

Now solve the equation n=\frac{0±\frac{8}{5}}{2} when ± is plus.

$$n=\frac{4}{5}$$

Now solve the equation n=\frac{0±\frac{8}{5}}{2} when ± is minus.

$$n=-\frac{4}{5}$$

The equation is now solved.

$$n=\frac{4}{5} n=-\frac{4}{5}$$