Question

given: \\(\left(x^{5}\
ight)\left(x^{4n}\
ight)\\). for what value of \\(n\\) is the given expression equivalent to \\(x^{13}\\)?
\\(n =\\)

Explanation:

Step1: Apply exponent product rule

When multiplying like bases, add exponents: $x^a \cdot x^b = x^{a+b}$. So,
$(x^5)(x^{4n}) = x^{5+4n}$

Step2: Set exponents equal

We want the result equal to $x^{13}$, so equate the exponents:
$5 + 4n = 13$

Step3: Solve for n

Subtract 5 from both sides:
$4n = 13 - 5 = 8$
Divide both sides by 4:
$n = \frac{8}{4} = 2$

Answer:

$n=2$