Let's fully simplify the given expression step-by-step:
We start with the given expression:
[tex]\[ 6 x^4 y^4 \left(8 x^3 y^2\right) \][/tex]
### Step 1: Distribute the constants and factors.
First, we focus on the numerical coefficients and the powers of [tex]\(x\)[/tex] and [tex]\(y\)[/tex].
Separately handle the numerical parts and the variable parts:
[tex]\[ 6 \cdot 8 \cdot x^4 \cdot x^3 \cdot y^4 \cdot y^2 \][/tex]
### Step 2: Multiply the coefficients.
Calculate the product of the constants 6 and 8:
[tex]\[ 6 \times 8 = 48 \][/tex]
### Step 3: Combine the exponents of the same base.
For the [tex]\(x\)[/tex] terms:
[tex]\[ x^4 \times x^3 \][/tex]
To combine these, we add their exponents:
[tex]\[ x^{4+3} = x^7 \][/tex]
For the [tex]\(y\)[/tex] terms:
[tex]\[ y^4 \times y^2 \][/tex]
To combine these, we add their exponents:
[tex]\[ y^{4+2} = y^6 \][/tex]
### Step 4: Combine everything into the simplified form.
Now put together the simplified numeric coefficient and the newly obtained powers of [tex]\(x\)[/tex] and [tex]\(y\)[/tex]:
[tex]\[ 48 x^7 y^6 \][/tex]
Thus, the fully simplified expression is:
[tex]\[ 48 x^7 y^6 \][/tex]
