Solve sqrt{2}*sqrt{2}-5^5div5^3+2^3^2

$$\sqrt{ 2 } \times \sqrt{ 2 } - { 5 }^{ 5 } \div { 5 }^{ 3 } + { 2 }^{ { 3 }^{ 2 } }$$

Evaluate

$$489$$

Solution Steps

Multiply \sqrt{2} and \sqrt{2} to get 2.

$$2-\frac{5^{5}}{5^{3}}+2^{3^{2}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 3 from 5 to get 2.

$$2-5^{2}+2^{3^{2}}$$

Calculate 5 to the power of 2 and get 25.

$$2-25+2^{3^{2}}$$

Subtract 25 from 2 to get -23.

$$-23+2^{3^{2}}$$

Calculate 3 to the power of 2 and get 9.

$$-23+2^{9}$$

Calculate 2 to the power of 9 and get 512.

$$-23+512$$

Add -23 and 512 to get 489.

$$489$$

Factor

$$3\times 163$$