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

In improper form your solution will be
`(90)/(7)`. As a mixed fraction it will be
`12(6)/(7)`.

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

=
`81\cdot (2)/(9)x^{(2)/(7)+(3)/(7)}` - Combine fractions
`(2)/(7)` and
`(3)/(7)`

=
`81\cdot (2)/(9)x^{(5)/(7)}` - Multiply the fractions, and simplify further

=
`\frac{162x^{(5)/(7)}}{9}` =
`18x^{(5)/(7)}` - This is out simplified expression

Now that we have this simplified expression, we can see that a =
`18`, and b =
`(5)/(7)`. Therefore, multiplying the two we should receive the improper fraction as follows,

`18 * (5)/(7)` =
`(90)/(7)` - Note that this is in improper form. If you want your solution in a mixed fraction, it will be
`12(6)/(7)`.