Answer:
-3
Step-by-step explanation:
To find:
The value of '?' in the following expression:
[tex]x^2y^8.x^3y^? = x^5y^5[/tex]
Solution:
First of all, let us have a look at a few rules of the exponents:
[tex]1.\ a^b.a^c=a^{b+c}[/tex]
[tex]2.\ a^b.a^{-c}=a^{b-c}[/tex]
Let us apply these rules and try to find out the missing value ('?') in the given expression.
Left Hand Side (LHS):
[tex]x^2y^8.x^3y^?\\\Rightarrow x^2.x^3.y^8.y^?\\\Rightarrow x^{2+3}y^{8+?}\\\Rightarrow x^{5}y^{8+?}[/tex]
Now, let us compare the LHS with RHS, we get:
[tex]x^{5}y^{8+?} = x^{5}y^{5}[/tex]
Dividing with [tex]x^5[/tex] on both sides:
[tex]y^{8+?} = y^5\\\Rightarrow 8+? = 5\\\Rightarrow ? = 5-8 \\\Rightarrow ? =-3[/tex]
Therefore, the missing value in the expression is -3.
