Gerardo is simplifying expressions with very large exponents. He arrives at each of the results below. For each result, decide if he is correct and justify your answer using the meaning of exponents.

1. $\frac{x^{150}}{x^{50}}⇒x^3$ 

   Hint (a):

   Remember to subtract the exponents when dividing terms with like bases.

   Answer (a):

   Not correct, the answer should be $x^{100}$. Make sure you are able to justify your answer.

2. $y^{20}·y^{41}⇒y^{61}$ 

   Hint (b):

   If you multiply $20\ y$'s together, and then multiply another $41$ to the original $20$, how many $y$'s are you multiplying together?

   Answer (b):

   $y^{61}$. Make sure you are able to justify your answer.

3. $\left(2m^2n^{15}\right)^3⇒2m^6n^{45}$ 

   Hint (c):

   Write down the expression inside the parentheses three times and then simplify as you did in part (b).