Let's solve the equation step by step to determine the missing term [tex]\( ? \)[/tex] in the equation:
[tex]\[ -60 x^5 y^3 = 5 x^3 y \cdot ? \][/tex]
To find the missing term, we'll isolate the question mark (?).
1. Divide both sides of the equation by [tex]\( 5 x^3 y \)[/tex]:
[tex]\[ \frac{-60 x^5 y^3}{5 x^3 y} = \frac{5 x^3 y \cdot ?}{5 x^3 y} \][/tex]
Simplifying the right side, we get:
[tex]\[ \frac{-60 x^5 y^3}{5 x^3 y} = ? \][/tex]
2. Simplify the left side of the equation step by step:
- Simplify the coefficients:
[tex]\[ \frac{-60}{5} = -12 \][/tex]
- Simplify the [tex]\( x \)[/tex]-terms:
[tex]\[ x^5 \div x^3 = x^{5-3} = x^2 \][/tex]
- Simplify the [tex]\( y \)[/tex]-terms:
[tex]\[ y^3 \div y = y^{3-1} = y^2 \][/tex]
3. Combine the simplified terms:
[tex]\[ \frac{-60 x^5 y^3}{5 x^3 y} = -12 x^2 y^2 \][/tex]
So, the missing term [tex]\( ? \)[/tex] is:
[tex]\[ ? = -12 x^2 y^2 \][/tex]
Therefore, the complete equation is:
[tex]\[ -60 x^5 y^3 = 5 x^3 y \cdot (-12 x^2 y^2) \][/tex]
