Answer:
see explanation
Step-by-step explanation:
Using the rules of exponents
[tex]a^{m}[/tex] × [tex]a^{n}[/tex] ⇔ [tex]a^{(m+n)}[/tex]
[tex]\frac{a^{m} }{a^{n} }[/tex] ⇔ [tex]a^{(m-n)}[/tex]
(5)
Split the factors into like terms
= [tex]\frac{10}{2}[/tex] × [tex]\frac{x^{7} }{x^{4} }[/tex] × [tex]\frac{y^{8} }{y^{3} }[/tex]
= 5 × [tex]x^{(7-4)}[/tex] × [tex]y^{(8-3)}[/tex]
= 5x³[tex]y^{5}[/tex]
(6)
Consider the left side
[tex]\frac{y^{(4+n)} }{y^2}[/tex] = [tex]y^{(4-2+n)}[/tex] = [tex]y^{2+n}[/tex], then
[tex]y^{2+n}[/tex] = [tex]y^{-3}[/tex]
Since the base on both sides is y, equate the exponents
2 + n = - 3 ( subtract 2 from both sides )
n = - 5
