Question

simplify. assume that no variable equals 0.

$(4d^2t^5v^{-4})(-5dt^{-3}v^{-1})$

options:

• $-dfrac{20d^3t^2}{v^5}$
• $dfrac{20d^3t^2}{v^5}$
• $-dfrac{d^3t^2}{20v^5}$
• $-20d^3t^2v^5$

Explanation:

Step1: Multiply the coefficients

Multiply the numerical coefficients: \(4 \times (-5) = -20\)

Step2: Multiply the \(d\)-terms

For the \(d\)-terms, use the rule \(a^m \times a^n = a^{m + n}\). So, \(d^2 \times d = d^{2 + 1} = d^3\)

Step3: Multiply the \(t\)-terms

For the \(t\)-terms, \(t^5 \times t^{-3} = t^{5 + (-3)} = t^{2}\)

Step4: Multiply the \(v\)-terms

For the \(v\)-terms, \(v^{-4} \times v^{-1} = v^{-4 + (-1)} = v^{-5}\). Since \(v^{-n}=\frac{1}{v^n}\), \(v^{-5}=\frac{1}{v^5}\)

Step5: Combine all terms

Combine the results from steps 1 - 4: \(-20 \times d^3 \times t^2 \times \frac{1}{v^5} = -\frac{20d^3t^2}{v^5}\)

Answer:

\(\boldsymbol{-\frac{20d^3t^2}{v^5}}\) (corresponding to the first option: \(-\frac{20d^3t^2}{v^5}\))