# How do you multiply #m^ { - 7/ 6} \cdot m ^ { 1/ 4}#?

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Recall the product rule for exponents:

When you are multiplying two powers with the same base, you add their exponent values together.

Applying the rule to the given question,

Since the fractions being added together do not have a common denominator, rewrite each fraction so that each one has the same denominator.

Evaluating,

However, expressions with negative exponents are usually simplified so that it only contains positive exponents.

Recall the negative exponent rule:

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To multiply (m^{-\frac{7}{6}} \cdot m^{\frac{1}{4}}), you add the exponents because they have the same base, which is (m).

So, [m^{-\frac{7}{6}} \cdot m^{\frac{1}{4}} = m^{-\frac{7}{6} + \frac{1}{4}}.]

To add the exponents, you need a common denominator. The common denominator for (6) and (4) is (12).

[= m^{-\frac{7}{6} + \frac{3}{12}}.]

Then, you convert (\frac{7}{6}) to an equivalent fraction with denominator (12).

[\frac{7}{6} = \frac{7 \times 2}{6 \times 2} = \frac{14}{12}.]

So, [= m^{-\frac{14}{12} + \frac{3}{12}}.]

Now, add the fractions.

[\frac{-14}{12} + \frac{3}{12} = -\frac{11}{12}.]

Thus, [m^{-\frac{7}{6}} \cdot m^{\frac{1}{4}} = m^{-\frac{11}{12}}.]

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