Certainly! Let's find the area of a rectangle when the length is given by [tex]\( 7xy^2 \)[/tex] and the width is given by [tex]\( 10x^2 \)[/tex].
To determine the area of a rectangle, we use the formula:
[tex]\[ \text{Area} = \text{Length} \times \text{Width} \][/tex]
Given:
- Length [tex]\( L = 7xy^2 \)[/tex]
- Width [tex]\( W = 10x^2 \)[/tex]
Now, we can substitute these expressions into the formula for the area:
[tex]\[ \text{Area} = (7xy^2) \times (10x^2) \][/tex]
To multiply these expressions, we multiply the coefficients and each variable separately:
1. Multiply the coefficients (the numerical values):
[tex]\[ 7 \times 10 = 70 \][/tex]
2. Multiply the [tex]\(x\)[/tex] terms:
[tex]\[ x \times x^2 = x^{1+2} = x^3 \][/tex]
3. Multiply the [tex]\(y\)[/tex] terms:
[tex]\[ y^2 \times 1 = y^2 \][/tex]
Putting it all together, the area [tex]\( A \)[/tex] becomes:
[tex]\[ \text{Area} = 70x^3y^2 \][/tex]
Thus, the area of the rectangle is:
[tex]\[ \boxed{70x^3y^2} \][/tex]
