Answer:
Part 1:- option first is correct
[tex]-\frac{1}{2}ab^{12}[/tex]
Part 1:- option third is correct
[tex]\frac{w^{10}}{3y^{4}}[/tex]
Step-by-step explanation:
Given:
The given ration expressions are.
1. [tex]\frac{-2a^{2}b^{4}}{4ab^{-8}}[/tex]
2. [tex]\frac{-5w^{4}y^{-2}}{-15w^{-6}y^{2}}[/tex]
We need to simplify the given expressions.
Solution:
Part 1:-
Given expression is
[tex]=\frac{-2a^{2}b^{4}}{4ab^{-8}}[/tex]
Using law of exponents [tex]\frac{x^{m} }{x^{n} } = x^{(m-n)}[/tex]
[tex]=-\frac{a^{2-1}b^{4-(-8)}}{2}[/tex]
[tex]=-\frac{a^{1}b^{4+8}}{2}[/tex]
[tex]=-\frac{ab^{12}}{2}[/tex]
[tex]=-\frac{1}{2}ab^{12}[/tex]
Therefore, option first [tex]-\frac{1}{2}ab^{12}[/tex] is correct.
Part 2:-
Given expression is.
[tex]=\frac{-5w^{4}y^{-2}}{-15w^{-6}y^{2}}[/tex]
Using law of exponents [tex]\frac{x^{m} }{x^{n} } = x^{(m-n)}[/tex]
[tex]=\frac{w^{4-(-6)}y^{-2-2}}{3}[/tex]
[tex]=\frac{w^{4+6}y^{-4}}{3}[/tex]
[tex]=\frac{w^{10}y^{-4}}{3}[/tex]
[tex]=\frac{w^{10}}{3y^{4}}[/tex]
Therefore, third option [tex]\frac{w^{10}}{3y^{4}}[/tex] is correct.
