Question

How do you write ${x^{ - 5}}{x^5}$ using a positive exponent?

Answer 1

We use the property of exponents that states that we can add the powers present on the numbers having the same bases. Here we have the same base x, so we add the powers and calculate the value in power.

• If a, m and n are any integer values then ${a^m} \times {a^n} = {a^{m + n}}$
• Any number having power 0 can be written as equal to 1 i.e. ${a^0} = 1$

Complete step-by-step answer:
We have to write the value of ${x^{ - 5}}{x^5}$ using a positive exponent
We know that when the bases are the same we can add the powers present on the numbers.
Here the base of both numbers ${x^{ - 5}}$ and ${x^5}$ is $x$, so we can write the value of the product by adding the powers .
$\Rightarrow {x^{ - 5}}{x^5} = {x^{ - 5 + 5}}$
Add the values in power
$\Rightarrow {x^{ - 5}}{x^5} = {x^0}$
Now the power of x is 0 which is a positive number.
We know that any number raised to power 0 is equal to 1
$\Rightarrow {x^{ - 5}}{x^5} = 1$
But we need our answer such that the number has a positive exponent. We know we can write 1 as ${x^0}$, so we write the final answer as ${x^0}$ because 0 is a positive number.

$\therefore$The value of ${x^{ - 5}}{x^5}$ using a positive exponent is ${x^0}$.

Note:
Many students make the mistake of writing the final answer as 1 as we know any number having the digit 0 in the power becomes 1. Keep in mind we are asked in the question to write the value using a positive number in the exponent which means we have to write the value in exponent form, so we write the value ${x^0}$ instead of 1.