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Yuki888 [10]
3 years ago
8

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

Mathematics
1 answer:
sweet-ann [11.9K]3 years ago
4 0

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 <em>-3.</em>

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