Question

How do you simplify ${10^a} \cdot {10^b} \cdot {10^c}$?

Answer 1

Hint: Given an exponential expression. We have to simplify the expression. First, we will apply the product rule of exponents to the expression. Add the exponents and write the expression in simplified form.

Formula used:
The product rule of exponent is given by:
${x^a} \cdot {x^b} = {x^{a + b}}$

Complete step-by-step answer:
We are given the expression. First apply the rule which states that if the base of the exponents are the same, then the exponents can be added.
Here, in the expression ${10^a} \cdot {10^b} \cdot {10^c}$, the base of each term is $10$ but the exponents are different.
Here, the given exponents are positive. Now, we will apply the product rule of exponents, we get:
$ \Rightarrow {10^a} \cdot {10^b} \cdot {10^c} = {10^{a + b + c}}$
Now, the expression cannot be simplified further.

Hence, the expression in simplified form is ${10^{a + b + c}}$.

Additional Information: When the expression is in the form of base and power, it is called exponential expression. If the expression contains multiplication of the same base and the exponents of the expression are positive integers, then the exponents of the expression are added by writing the base once. The exponents are used to show how many times the number is multiplied. Here ${10^a}$ shows that number $10$ is multiplied by $10$, $a$ times. Then after adding the exponents the number is multiplied by itself the sum of the exponents times.

Note:
In such types of questions the students mainly don't get an approach on how to solve it. In such types of questions students are mainly confused while applying the correct law of exponents and how to simplify the expression.