Write the quotient with positive exponents.

StartFraction 10 m squared n Superscript 4 Over 16 m Superscript 6 Baseline n squared EndFraction10m2n416m6n2

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Part 1

StartFraction 10 m squared n Superscript 4 Over 16 m Superscript 6 Baseline n squared EndFraction10m2n416m6n2equals=enter your response here

​(Simplify your answer. Use integers or fractions for any numbers in the​ expression.)

To simplify the expression \(\frac{10 m^2 n^4}{16 m^6 n^2}\) with positive exponents, follow these steps:

### Step 1: Simplify the coefficients
\[
\frac{10}{16} = \frac{5}{8}
\]

### Step 2: Simplify the \( m \) terms
\[
\frac{m^2}{m^6} = m^{2-6} = m^{-4}
\]

### Step 3: Simplify the \( n \) terms
\[
\frac{n^4}{n^2} = n^{4-2} = n^2
\]

### Step 4: Combine the simplified terms
\[
\frac{5}{8} \cdot m^{-4} \cdot n^2 = \frac{5 n^2}{8 m^4}
\]

### Final Answer
\[
\frac{10 m^2 n^4}{16 m^6 n^2} = \frac{5 n^2}{8 m^4}
\]

Would you like more details on this solution or have any questions?

Here are 5 related questions you might find useful:
1. How do you simplify expressions with negative exponents?
2. What are the properties of exponents used in division?
3. How do you convert a negative exponent to a positive one?
4. What is the general rule for simplifying fractional exponents?
5. How do you simplify algebraic fractions with multiple variables?

**Tip:** When dividing like bases with exponents, subtract the exponents of the denominator from those of the numerator.

Write the quotient with positive exponents. StartFraction 10 m squared n Superscript 4 Over 16 m Superscript 6 Baseline n squared EndFraction10m2n416m6n2equals(Simplify your answer. Use integers or fractions for any numbers in the expression.)

Learn how to simplify the algebraic expression 10m²n⁴/16m⁶n² with step-by-step instructions. This problem covers key concepts like exponent rules and algebraic fraction simplification. Ideal for students in Grades 8-10.

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