Question

What is the value of 7 to the fifth power?

Answer 1

Hint: Raising any number to the $n^{th}$ power, where n is a natural number, means we have to multiply that number $n$ times by itself. Here we are given the value of 7 and we are required to raise it to the power of 5, so in short we need to multiply 7 by itself and we have to do it 5 times continuously.

Complete step-by-step answer:
We need to calculate the value of 7 to the $5^{th}$ power. For any number $a$ if we are calculating the power of it to the $n^{th}$ time, in mathematical terms it means we are calculating:
$a^n=a \times a\times\ldots a$ ($n$ times)
Here the value of $a$ is 7 and the value of $n$ is 5. We plug in the values and we obtain the following:
$7^5=7\times 7\times7\times7\times7$
Calculating this we obtain:
$7^5=49 \times 49 \times 7$
$\implies 7^5=16807$
Hence the value of 7 raised to the fifth power has been calculated.

Note: For such large calculations, you need to be very aware while performing the operations. So, your calculations should be very precise. You can take help of some identities as well, for example, in this case since you are required to find the square of 49 you can write:
$49^2=\left(50-1\right)^2$
and then use the following formula:
$\left(a-b\right)^2=a^2+b^2+2ab$
You will obtain the result faster and more accurate in this way. You can apply the same trick while calculating the cube as well if you somehow encounter a value whose cube is to be found out.