Question

what value of $n$ makes the statement true?
$6x^{n} \cdot 4x^{2} = 24x^{6}$
$n = \square$

Explanation:

Step1: Multiply the coefficients

$6 \times 4 = 24$

Step2: Apply exponent product rule

For $x^n \cdot x^2$, use $x^a \cdot x^b = x^{a+b}$, so we get $x^{n+2}$

Step3: Set up exponent equation

Match the exponents of $x$: $n + 2 = 6$

Step4: Solve for n

$n = 6 - 2$

Answer:

$4$