Question

simplify.
3y^{-10}n^{-1} cdot 6y^{9}n^{3} cdot 5v^{2}
use only positive exponents in your answer.

Explanation:

Step1: Multiply constant coefficients

$3 \times 6 \times 5 = 90$

Step2: Combine $y$ terms via exponent addition

$y^{-10} \times y^{9} = y^{-10+9} = y^{-1}$

Step3: Combine $u$ terms via exponent addition

$u^{-1} \times u^{3} = u^{-1+3} = u^{2}$

Step4: Combine $v$ terms via exponent addition

$v^{2} \times v^{1} = v^{2+1} = v^{3}$

Step5: Rewrite negative exponents positively

$y^{-1} = \frac{1}{y}$

Step6: Combine all simplified terms

$90 \times \frac{1}{y} \times u^{2} \times v^{3}$

Answer:

$\frac{90u^{2}v^{3}}{y}$