Question

What is 10 to the fifth power?

Answer 1

Hint: To find the value of 10 to the fifth power, we will denote it as ${{10}^{5}}$ . When a number, say, x, is raised to a number, say a, we can find its value by multiplying x, ‘a’ times.

Complete step by step solution:
We have to find the value of 10 to the fifth power. Let us denote this as ${{10}^{5}}$ . We know that for a number, say, x, when raised to a number, say a, we can find its value by multiplying x, ‘a’ times. We can write it as
${{x}^{a}}=\underbrace{x\times x\times ....\times x}_{a\text{ times}}$
Hence, we can write ${{10}^{5}}$ as
${{10}^{5}}=10\times 10\times 10\times 10\times 10$
Let us simplify the above value. First, we have to combine pairs of 10.
$\Rightarrow {{10}^{5}}=\left( 10\times 10 \right)\times \left( 10\times 10 \right)\times 10$
Let us multiply each pair.
$\Rightarrow {{10}^{5}}=100\times 100\times 10$
Now, we have a combined pair of 100.
$\Rightarrow {{10}^{5}}=\left( 100\times 100 \right)\times 10$
Let us multiply this pair of 100.
$\Rightarrow {{10}^{5}}=10000\times 10$
Now, let us perform a multiplication operation.
$\Rightarrow {{10}^{5}}=100000$

Hence, the value of 10 to the fifth power is 100000.

Note: Students must note that when a question contains ‘to the power of’ and ‘raised to’, it means we are dealing with exponents. For a number in the form ${{10}^{5}}$ , we call 5 as the exponent and 10 as the base. An exponent refers to the number of times a number is multiplied by itself. We can also find ${{10}^{5}}$ in an alternate way. Instead of multiplying 10 five times, we just need to add five zeroes to the right of 1. There are many properties associated with exponents.