Question

What is the positive difference between 3 to the ${{5}^{th}}$ power and 5 to the ${{3}^{rd}}$ power?

Answer 1

Hint: To obtain the positive difference between 3 to the ${{5}^{th}}$ power and 5 to the ${{3}^{rd}}$ power we will find the simplified form of both and then subtract them to get our desired answer. One thing is to be kept in mind is that a smaller number should be subtracted from the bigger number for getting the positive answer.

Complete step by step solution:
To find the positive difference between the two numbers given we will write them in proper form as below:
3 to the ${{5}^{th}}$ power can be written as
 $={{3}^{5}}$
5 to the ${{3}^{rd}}$ power can be written as
$={{5}^{3}}$
Now, we will simplify first values written above as:
$\Rightarrow {{3}^{5}}=3\times 3\times 3\times 3\times 3$
$\therefore {{3}^{5}}=243$…….$\left( 1 \right)$
Next, we will simplify second value written above as:
$\Rightarrow {{5}^{3}}=5\times 5\times 5$
$\therefore {{5}^{3}}=125$…….$\left( 2 \right)$
We will subtract equation (2) from equation (1) and get,
$\begin{align}
  & \Rightarrow {{3}^{5}}-{{5}^{3}}=243-125 \\
 & \therefore {{3}^{5}}-{{5}^{3}}=118 \\
\end{align}$

Hence, the positive difference between 3 to the ${{5}^{th}}$ power and 5 to the ${{3}^{rd}}$ power is 118.

Note: Exponential notation is used to write the repeated multiplication more properly. The number with the same base when multiplied there power is added this is what we call exponential notation of the number multiplied. As ${{2}^{3}}$is read as “2 to the third power” which means $2\times 2\times 2$ which gives the answer 8. When the exponent is 0 then we always get the answer as 1 and when the exponent of a number is 1 we get the number itself. When the exponent has a negative sign then the number becomes a fraction with numerator 1 and denominator as that number with the exponent without the negative sign.