Question

How do you get from x^-3 to x^1

please explain your answer

Answer 1

Multiply by

`x.x.x.x`

Explanation:

Moving from x‐³ to x¹ requires an increase in the index of the variable. This can be done by multiplying like variables together thus adding the indices.

Multiplying any 2 like terms, is just as good as adding the indices of the the two terms while maintaining a single base. For example:

`{2}^(1) * {2}^(1) = {2}^(1 + 1) \\ = {2}^(2) \\ = 4`

Similarly:

`{y}^(5) * {y}^(8) = {y}^(5 + 8) \\ = {y}^(13)`

NB: THIS CAN ONLY BE DONE WHEN THERE ARE LIKE TERMS OR SIMILAR BASES.

Therfore to find how many x's you need to multiply by to move from x-³ to x¹ is just as good as saying:

`a + ( - 3) = 1`

{where a represents the index of the variable}

`a - 3 = 1 \\ a - 3 + 3 = 1 + 3 \\ a = 4`

therfore the index of the variable will be 4.

x⁴

Thus you have to multiply x-³ by x four times to get to x¹ which is simply the same as Multiplying by

`x.x.x.x`