Question

question 1-2
the expression
\\(\left(3^{\frac{4}{7}}\
ight)\left(3^{\frac{3}{7}}\
ight)\\)
can be rewritten as \\(3^k\\) where \\(k\\) is a constant. what is the value of \\(k\\)?

Explanation:

Step1: Apply exponent product rule

When multiplying exponential terms with the same base, add exponents: $a^m \cdot a^n = a^{m+n}$. Here, the base is 3, so:
$3^{\frac{6}{7}} \cdot 3^{\frac{8}{7}} = 3^{\frac{6}{7}+\frac{8}{7}}$

Step2: Add the fractions

Add the numerators over the common denominator:
$\frac{6}{7}+\frac{8}{7} = \frac{6+8}{7} = \frac{14}{7} = 2$

Answer:

$2$