Question

How do you simplify $ ({x^5})({x^6}) $ ?

Answer 1

Hint: In order to determine the value of the above question ,use exponent property . But the question arises what is exponent , so the answer to this is that the base $ 'a' $ raised to the power of n is equal to the multiplication of ‘a’ , n times. \[{a^{\;n}}\; = \;a\; \times \;a\; \times \;...\; \times \;a\]…..upto n times.
Exponent property states that when we are to multiply the two bases that have the same value then we can also add the powers or exponents . Similarly , when we are to divide the two bases that have the same value then we can also subtract the powers or exponents . Adding or subtracting the exponents makes the solution easier and way short.
 $ {a^{b + c}} = {a^b}{a^c} $

Complete step-by-step answer:
Applying the above exponent rule in this question, we get:
 $ {a^{b + c}} = {a^b}{a^c} $
 $ \dfrac{{{a^b}}}{{{a^c}}} = {a^{b - c}} $
To solve the given question, we must know the properties of exponents and with the help of them we are going to rewrite our question.
But we also need to know that the number or the base must have the same value otherwise we cannot apply the exponent or product rule.
First, we are going to rewrite and solve with the help of the properties of product rule
 $ {x^{5 + 6}} = ({x^5})({x^6}) $
 with same base are equal , therefore powers are added and we can write it in simplified manner as
 $ {x^{5 + 6}} $
Also we can do sum of exponents getting the answer as,
 $ {x^{11}} $
Therefore ,simplification of $ ({x^5})({x^6}) $ is $ {x^{11}} $ .
So, the correct answer is “ $ {x^{11}} $ .”.

Note: Don’t forget to cross check your result.
Remember this point while dealing with laws of indices related problems.
Any number raised to the power of ‘1’ is always equal to the number itself.
Any number raised to the power of ‘0’ is always equal to the number ‘1’ .
The number one raised to any power is always ‘1’ .