Question

What value of n makes the statement true? 6xn · 4x2 = 24x6

Answer 1

We check first the numerical coefficients of both sides of the equation if they match if we perform the operation.
                        (6)(4) = 24
Then, the variables. For multiplication with the same variables, the exponents are added. In the given above,
                                 n + 2 = 6
The value of n should be 4. 

Answer 2

To find the value of n we have to use power law. The value of n that makes the statement true is 4.

Given:

Expression is $6x^n \times 4x^2=24x^6$

It is required to get the value of n from the given expression.

Apply the power law to the given expression as:

$6x^n \times 4x^2=24x^6\\ 24x^{n+2}=24x^6 \;\{a^m\cdot a^n=a^{m+n}\}$

As per power law, we know that:

$a^m=a^n\Rightarrow m=n\\n+2=6 n=6-2\\n=4$

Hence, value of n that makes the statement true is 4.

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