Question

How to solve this.
(225)^2.5÷225

Answer 1

As, there is nothing on 225 so we consider it is raised to power 1.
$225 ^{2.5} \div 225 \\ = 225 ^{2.5} \div {225}^{1}$

Now, By using Law of Exponent where bases are same and powers are different in division, we subtract the powers.

$(225) ^{2.5 - 1}$
$225 ^{1.5}$
Now, 1.5 can be written as 15/10 and 225 can be written as 15^2

$= 225 ^{ \frac{15}{10} } \\ = (15 ^{2} ) ^{ \frac{15}{10} } \\ = (15) ^{2 \times \frac{15}{10} } \\ = {15}^{3} = 3375$