Question

When (81x^2/7) (2/9x^3/7) is simplified, it can be written in the form ax^b where a and b are real numbers. Find ab.

Answer 1

Answer:

In improper form your solution will be $\frac{90}{7}$. As a mixed fraction it will be $12\frac{6}{7}$.

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,

$\left(81x^{\frac{2}{7}}\right)\:\left(2/9x^{\frac{3}{7}}\right)\:$ - Apply exponential rule " $\:a^b\cdot \:a^c=a^{b+c}$ "

= $81\cdot \frac{2}{9}x^{\frac{2}{7}+\frac{3}{7}}$ - Combine fractions $\frac{2}{7}$ and $\frac{3}{7}$

= $81\cdot \frac{2}{9}x^{\frac{5}{7}}$ - Multiply the fractions, and simplify further

= $\frac{162x^{\frac{5}{7}}}{9}$ = $18x^{\frac{5}{7}}$ - This is out simplified expression

Now that we have this simplified expression, we can see that a = $18$, and b = $\frac{5}{7}$. Therefore, multiplying the two we should receive the improper fraction as follows,

$18 * \frac{5}{7}$ = $\frac{90}{7}$ - Note that this is in improper form. If you want your solution in a mixed fraction, it will be $12\frac{6}{7}$.