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:
\(a^m=a^n\Rightarrow m=n\
+2=6 n=6-2\
=4\)
Hence, value of n that makes the statement true is 4.
Learn more about Laws of exponent here:
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