Sure, let's start by simplifying the expression given in part (a).
### Step-by-Step Solution:
We are given the expression:
[tex]$
\frac{5 x^5 y^6}{x^2 y^4}
$[/tex]
Step 1: Simplifying the numerator and the denominator separately
Step 2: Breaking down the exponents
First, let's consider the [tex]\(x\)[/tex] terms in both the numerator and denominator:
[tex]$
\frac{x^5}{x^2}
$[/tex]
By the laws of exponents, when we divide like bases, we subtract the exponents:
[tex]$
x^{5-2} = x^3
$[/tex]
Next, consider the [tex]\(y\)[/tex] terms in both the numerator and denominator:
[tex]$
\frac{y^6}{y^4}
$[/tex]
Similarly, using the laws of exponents, we subtract the exponents:
[tex]$
y^{6-4} = y^2
$[/tex]
Step 3: Combining all simplified terms
Now, let's place the simplified terms back into the expression:
[tex]$
\frac{5 x^5 y^6}{x^2 y^4} = 5 x^3 y^2
$[/tex]
So, the simplified form of the given expression is:
[tex]$
5 x^3 y^2
$[/tex]
And that's the final simplified form of the expression!
