How do you simplify the expression $\frac{y^{4}}{y^{- 7}}$ $y^4/y^-7$ using the properties?

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Answer 1 · 2017-07-18T05:46:05

$\frac{y^{4}}{y^{- 7}} = y^{11}$ $y^4/y^(-7)=y^11$

Given -

$\frac{y^{4}}{y^{- 7}}$ $y^4/y^(-7)$

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

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

Then

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

Answer 2 · 2017-07-18T08:37:55

$y^{11}$ $y^11$

Recall the law of indices for division.

$\frac{x^{m}}{x^{n}} = x^{m - n} \leftarrow$ $x^m/x^n = x^(m-n)" "larr$ subtract the indices

$\frac{y^{4}}{y^{- 7}} = y^{4 - (- 7)}$ $y^4/y^-7 = y^(4-(-7)$

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

$= y^{11}$ $=y^11$

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

How do you simplify the expression y4y−7y^4/y^-7 using the properties?