Question

How do you write “16” as a power two different ways?

Answer 1

Hint:Power to a number means the same number is multiplied to the number of times the power is present, for example if given that two has power of four, then it means two is multiplied four times. You should know a number power zero means one.

Complete step by step answer:
The given question is to write the given in numbers as a power of two different ways, lets first find the factors of the given number, on solving we get:
\[factors\,of\,16 = 1 \times 2 \times 2 \times 2 \times 2 = 4 \times 4 = 8 \times 2 = 16 \times 1\]
Here we obtain the factors of the given number, we can see that here two factors are present that is two and four which occur in pairs and independently complete the number sixteen by multiplying itself by a number of times.

So our required number can be written as, the power of two and power of four, for two the power would be four because on multiplying two, four times we can obtain sixteen and for four the power would be two because multiplying four two times would give sixteen,
Expressing the above statement in mathematical form, on solving we get:
\[ 16 = 2 \times 2 \times 2 \times 2 = {2^4} \\
\therefore 16 = 4 \times 4 = {4^2}\]
Here we got our answer in the form of power.

Note:To obtain the number in terms of power to any other number we have to see that the given number should have pair of factors, as we can give power to any number when it is multiplied by itself, that is if two is multiplied by two then we can write four equals two power two.