Let's go through solving the given expression step-by-step:
The given expression is:
[tex]\[ \frac{(-s^2 t) \times (-s t^2)}{-s^2 t^2} \][/tex]
First, let's handle the numerator. We need to multiply:
[tex]\[ (-s^2 t) \times (-s t^2) \][/tex]
Recall the distributive property of multiplication over addition and how we handle negative signs:
- A negative times a negative is a positive.
- We will multiply the coefficients (numerical parts) and the variables separately.
So, multiply the coefficients:
[tex]\[ (-1)(-1) = 1 \][/tex]
Next, multiply the variables:
[tex]\[ s^2 \times s = s^{2+1} = s^3 \][/tex]
And for the [tex]\( t \)[/tex] terms:
[tex]\[ t \times t^2 = t^{1+2} = t^3 \][/tex]
Combining these, the numerator becomes:
[tex]\[ (-s^2 t) \times (-s t^2) = s^3 t^3 \][/tex]
Now our expression is:
[tex]\[ \frac{s^3 t^3}{-s^2 t^2} \][/tex]
Now we will simplify the denominator:
The denominator is already in a simplified form as:
[tex]\[ -s^2 t^2 \][/tex]
We now handle the division by subtracting the powers of like terms in the numerator and the denominator:
[tex]\[ \frac{s^3 t^3}{-s^2 t^2} \][/tex]
For the [tex]\( s \)[/tex] terms:
[tex]\[ \frac{s^3}{s^2} = s^{3-2} = s^1 = s \][/tex]
For the [tex]\( t \)[/tex] terms:
[tex]\[ \frac{t^3}{t^2} = t^{3-2} = t^1 = t \][/tex]
And don't forget the negative sign in the denominator, which affects the final result:
[tex]\[ \frac{s^3 t^3}{-s^2 t^2} = -s t \][/tex]
Therefore, the simplified form of the expression:
[tex]\[ \frac{(-s^2 t) \times (-s t^2)}{-s^2 t^2} \][/tex]
is:
[tex]\[ -s t \][/tex]
