Question

What is 1 over 2 to the ${{5}^{th}}$ power?

Answer 1

Hint: Assume the given expression as E. Now, we will write the mathematical form of the given sentence. Further we will simplify the expression using the formula of exponents given as ${{\left( \dfrac{a}{b} \right)}^{m}}=\dfrac{{{a}^{m}}}{{{b}^{m}}}$ where m is the exponent 5. Finally we will multiply the numerator 5 times with itself to get the resultant numerator and similarly we will multiply the denominator 5 times with itself to get the resultant denominator. The obtained fraction will be our answer.

Complete step by step solution:
Here we have been asked to find the value of 1 over 2 to the ${{5}^{th}}$ power. First we need to write the mathematical form of this expression. Let us assume this expression as E.
Now, we have the first term 1 over 2 that means it is a fraction with 1 as the numerator and as the denominator. The second term is to the ${{5}^{th}}$ power that means this fraction is raised to the power 5 as a whole. So the mathematical expression can be written as:
$\Rightarrow E={{\left( \dfrac{1}{2} \right)}^{5}}$
Breaking the terms by using the formula of exponents given as ${{\left( \dfrac{a}{b} \right)}^{m}}=\dfrac{{{a}^{m}}}{{{b}^{m}}}$ we get,
$\Rightarrow E=\dfrac{{{1}^{5}}}{{{2}^{5}}}$
This ${{5}^{th}}$ power denotes that we have to multiply the number 5 times with the number itself, so we get,
$\begin{align}
  & \Rightarrow E=\dfrac{1\times 1\times 1\times 1\times 1}{2\times 2\times 2\times 2\times 2} \\
 & \therefore E=\dfrac{1}{32} \\
\end{align}$

Hence $\dfrac{1}{32}$ is the answer.

Note: You must understand different mathematical terms so that you can convert a statement into an expression. If you will form the wrong expression then the outcome will be wrong. Remember all the formulas of exponents as they are used everywhere in mathematics. Remember that the exponent denotes nothing but the number of times an expression must be multiplied with itself.