Answer:
In improper form your solution will be [tex]\frac{90}{7}[/tex]. As a mixed fraction it will be [tex]12\frac{6}{7}[/tex].
Step-by-step explanation:
The first thing we want to do here is to simplify this expression. After doing so, " a " and " b " should be multiplied to result in a possible improper fraction,
[tex]\left(81x^{\frac{2}{7}}\right)\:\left(2/9x^{\frac{3}{7}}\right)\:[/tex] - Apply exponential rule " [tex]\:a^b\cdot \:a^c=a^{b+c}[/tex] "
= [tex]81\cdot \frac{2}{9}x^{\frac{2}{7}+\frac{3}{7}}[/tex] - Combine fractions [tex]\frac{2}{7}[/tex] and [tex]\frac{3}{7}[/tex]
= [tex]81\cdot \frac{2}{9}x^{\frac{5}{7}}[/tex] - Multiply the fractions, and simplify further
= [tex]\frac{162x^{\frac{5}{7}}}{9}[/tex] = [tex]18x^{\frac{5}{7}}[/tex] - This is out simplified expression
Now that we have this simplified expression, we can see that a = [tex]18[/tex], and b = [tex]\frac{5}{7}[/tex]. Therefore, multiplying the two we should receive the improper fraction as follows,
[tex]18 * \frac{5}{7}[/tex] = [tex]\frac{90}{7}[/tex] - Note that this is in improper form. If you want your solution in a mixed fraction, it will be [tex]12\frac{6}{7}[/tex].
