Express the following fraction in simplest form using only positive exponents.
start fraction, 5, left parenthesis, v, right parenthesis, cubed, divided by, 3, v, end fraction
3v
5(v)
3

​

To simplify the given expression, which is:

\[
\frac{5v^3}{3v}
\]

Follow these steps:

1. **Divide the coefficients:** The coefficients 5 and 3 remain as they are because they do not simplify further.

2. **Simplify the exponents:** Use the rule \( \frac{a^m}{a^n} = a^{m-n} \). Here, the base is \( v \), with exponents 3 and 1, respectively.
   \[
   v^{3-1} = v^2
   \]

3. **Combine the results:** The simplified expression is:

\[
\frac{5v^2}{3}
\]

So, the expression in simplest form with only positive exponents is:

\[
\frac{5v^2}{3}
\]

Would you like more details or have any questions? Here are 8 related questions:

1. How do you simplify an expression with negative exponents?
2. What is the rule for dividing powers with the same base?
3. Can you simplify \(\frac{8x^4}{4x^2}\)?
4. What is the simplified form of \(\frac{12a^5}{6a^2}\)?
5. How do you multiply fractions with variables?
6. What happens if the exponent in the denominator is larger than in the numerator?
7. Can you express \(\frac{7y^3}{y}\) in simplest form?
8. How do you handle exponents in a fraction where the numerator is a polynomial?

**Tip:** When dividing terms with the same base, subtract the exponent in the denominator from the exponent in the numerator.

Learn how to simplify the fraction (5v³) / (3v) into its simplest form using positive exponents. Follow a step-by-step explanation of dividing coefficients and simplifying exponents. Suitable for Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation