# How do you simplify the expression y^4/y^-7 using the properties?

Jul 18, 2017

${y}^{4} / {y}^{- 7} = {y}^{11}$

#### Explanation:

Given -

${y}^{4} / {y}^{- 7}$

${a}^{b} = \frac{1}{a} ^ \left(- b\right)$

Hence $\frac{1}{y} ^ \left(- 7\right) = {y}^{7}$

Then

$y = {y}^{4} \times {y}^{7} = {y}^{4 + 7} = {y}^{11}$
${y}^{11}$

Jul 18, 2017

${y}^{11}$

#### Explanation:

Recall the law of indices for division.

${x}^{m} / {x}^{n} = {x}^{m - n} \text{ } \leftarrow$ subtract the indices

y^4/y^-7 = y^(4-(-7)

$= {y}^{4 + 7}$

$= {y}^{11}$

However, my first method of choice would be to change the negative index to a positive one by using the method shown by contributor nallasivan V