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mylen [45]
3 years ago
10

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.

Mathematics
1 answer:
larisa86 [58]3 years ago
5 0

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}.

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