Examkin

Question

Difficulty: EasyOperations with Variable Exponents

Calculate the product of the two algebraic terms below:

−4m3×3m4 -4m^3 \times 3m^4

What is the correct result of this multiplication?

  1. −12m7-12m^7Answer
  2. B
    12m712m^7
  3. C
    −12m12-12m^{12}
  4. D
    12m1212m^{12}

Answer

The correct answer is −12m7-12m^7.
To multiply these terms, first multiply the numerical coefficients: −4×3=−12-4 \times 3 = -12. Then, apply the product rule for exponents by adding the exponents of the common base mm: 3+4=73 + 4 = 7. Combining these yields −12m7-12m^7.

Step-by-Step Solution

1
Multiply the numerical coefficients.
−4×3=−12-4 \times 3 = -12
When multiplying algebraic terms, the constant factors are multiplied together using standard integer rules.
2
Apply the product rule for exponents to the variables.
m3×m4=m3+4=m7m^3 \times m^4 = m^{3+4} = m^7
The product rule states that when multiplying terms with the same base, their exponents should be added.
3
Combine the coefficient and the variable part.
−12m7-12m^7
Putting the results from the previous steps together gives the final simplified expression.

Key Concept

Product Rule for Exponents and Multiplying Monomials
Estimated Time:45s
Rate this question

Topics

Operations with Variable Exponents

More questions from this topic