To solve the equation \( 10m^5 = -640m^2 \), follow these steps:

### Step 1: Divide both sides by \( m^2 \)
We can simplify the equation by dividing both sides by \( m^2 \), assuming \( m \neq 0 \):

\[
\frac{10m^5}{m^2} = \frac{-640m^2}{m^2}
\]

This simplifies to:

\[
10m^3 = -640
\]

### Step 2: Divide both sides by 10
Next, divide both sides by 10 to further simplify the equation:

\[
m^3 = \frac{-640}{10}
\]

This gives:

\[
m^3 = -64
\]

### Step 3: Take the cube root of both sides
Now, solve for \( m \) by taking the cube root of both sides:

\[
m = \sqrt[3]{-64}
\]

Since \( \sqrt[3]{-64} = -4 \), we have:

\[
m = -4
\]

### Final Answer:
The solution to the equation is:

\[
m = -4
\]

Would you like more details on any of the steps, or have any questions?

Here are 5 related questions:
1. How do you solve equations with higher powers of variables like \( m^5 \)?
2. What are the general rules for simplifying powers of variables?
3. How can you apply cube roots to both positive and negative numbers?
4. What happens if \( m = 0 \) in the original equation?
5. How would you solve if there were fractions instead of integers?

**Tip:** Always check if your solution satisfies the original equation by plugging it back in.

Explore how to solve the polynomial equation 10m^5 = -640m^2 step-by-step by simplifying powers and applying cube roots. This guide includes algebraic concepts like exponents and cube roots. Perfect for students in Grades 9-11.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation