Math Problem Statement

Solution

The expression shown in the image is:

mn9m3\frac{mn^9}{m^3}

To simplify this expression:

  1. Identify and simplify similar terms: Here, the variable mm appears in both the numerator and the denominator.
  2. Apply the exponent rules: Specifically, use the rule aman=amn\frac{a^m}{a^n} = a^{m-n}.

Let's simplify:

mn9m3=m13n9\frac{mn^9}{m^3} = m^{1-3} \cdot n^9

This simplifies to:

m2n9m^{-2}n^9

Alternatively, the simplified expression can be written as:

n9m2\frac{n^9}{m^2}

So, the simplified expression is n9m2\frac{n^9}{m^2}.

Would you like further details on this, or do you have any questions?

Here are 5 related questions:

  1. How do you simplify a5b3a2b2\frac{a^5b^3}{a^2b^2}?
  2. What is the simplified form of c7dc2\frac{c^7d}{c^2}?
  3. How would you handle the simplification of p4q2p4q3\frac{p^4q^2}{p^4q^3}?
  4. How do you simplify expressions with negative exponents like x3y2x^{-3}y^{-2}?
  5. What is the rule for multiplying exponents with the same base?

Tip: When simplifying expressions with exponents, always subtract the exponents when dividing terms with the same base.