Simplify fully: $$ \frac{\left(2 m^{2} ight)^{2}+3 m^{3} imes 2 m}{4 m^{5}} $$

Question

Simplify fully: $$ \frac{\left(2 m^{2}ight)^{2}+3 m^{3} 	imes 2 m}{4 m^{5}} $$

UpStudy AI · Accepted Answer

1. Simplify the first term in the numerator:
   $$
   \left(2 m^2\right)^2 = 2^2 \cdot \left(m^2\right)^2 = 4 m^4.
   $$

2. Simplify the second term in the numerator:
   $$
   3 m^3 \times 2 m = 6 m^{3+1} = 6 m^4.
   $$

3. Combine the terms in the numerator:
   $$
   4 m^4 + 6 m^4 = 10 m^4.
   $$

4. Write the original expression with the simplified numerator:
   $$
   \frac{10 m^4}{4 m^5}.
   $$

5. Simplify the expression by dividing the coefficients and subtracting the exponents of $$ m $$:
   $$
   \frac{10}{4} \cdot m^{4-5} = \frac{10}{4} \cdot m^{-1}.
   $$
   
6. Simplify the fraction and rewrite $$ m^{-1} $$:
   $$
   \frac{10}{4} = \frac{5}{2} \quad \text{and} \quad m^{-1} = \frac{1}{m}.
   $$
   
7. The final simplified expression is:
   $$
   \frac{5}{2 m}.
   $$
The simplified expression is $$ \frac{5}{2m} $$.

Simplify fully:

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