Question

What is the missing value in x2y8 · x3y? = x5y5?

Answer 1

Answer:

-3

Step-by-step explanation:

To find:

The value of '?' in the following expression:

$x^2y^8.x^3y^? = x^5y^5$

Solution:

First of all, let us have a look at a few rules of the exponents:

$1.\ a^b.a^c=a^{b+c}$

$2.\ a^b.a^{-c}=a^{b-c}$

Let us apply these rules and try to find out the missing value ('?') in the given expression.

Left Hand Side (LHS):

$x^2y^8.x^3y^?\\\Rightarrow x^2.x^3.y^8.y^?\\\Rightarrow x^{2+3}y^{8+?}\\\Rightarrow x^{5}y^{8+?}$

Now, let us compare the LHS with RHS, we get:

$x^{5}y^{8+?} = x^{5}y^{5}$

Dividing with $x^5$ on both sides:

$y^{8+?} = y^5\\\Rightarrow 8+? = 5\\\Rightarrow ? = 5-8 \\\Rightarrow ? =-3$

Therefore, the missing value in the expression is -3.