Question

what is half of 2 to the ${{6}^{th}}$ power.

Answer 1

Hint: Now first we will find the value of half of 2 to the ${{6}^{th}}$ power. Now once we have the value of ${{2}^{6}}$ we will multiply the value by $\dfrac{1}{2}$ . hence we will obtain the value of half of 2 to the ${{6}^{th}}$ power.

Complete step by step solution:
Now let us first understand the concept of the exponents.
Now in general exponents are written in the form of ${{a}^{n}}$ where n is called the power of a.
Now let us understand what this power means. Power is a number raised to some number. Power denotes how many times the number which it is raised to should be multiplied by itself.
Hence let us say we have ${{2}^{3}}$ . Here we have 3 raised to 2 hence the power of 3 is 2. Hence the number 2 should be multiplied by itself 3 times. Hence we get, ${{2}^{3}}=2\times 2\times 2=8$ .
Now let us consider the given problem.
We want to find ${{6}^{th}}$ power of 2.
$\Rightarrow {{2}^{6}}=2\times 2\times 2\times 2\times 2\times 2$
$\Rightarrow {{2}^{6}}=64$
Now let us multiply the equation by $\dfrac{1}{2}$. Hence we get,
$\Rightarrow 64\times \dfrac{1}{2}=32$
Hence the value of half of 2 to the ${{6}^{th}}$ power is 32.

Note: Now note that power of a number can also be negative or zero. Now any number raised to 0 is 1 and if the power is negative we can convert it into positive by using the property ${{a}^{-n}}=\dfrac{1}{{{a}^{n}}}$ . We can also directly solve the expression as $\dfrac{1}{2}\times {{2}^{6}}={{2}^{5}}$.