We want to divide the given rational expressions.
3x^3/5y^2÷ 6y^(-3)/5x^(-5)
To divide the expressions, let's recall the Negative Exponent Property.
x^(- n)=1/x^nThis property can be rewritten for cases where we have a negative exponent in the denominator.
1/x^(- n)=x^n
Let's use the above to start simplifying the expressions.
We will also split the numerators and denominators of both expressions into factors to cancel out any common factors.
To divide the expressions, we will multiply the first expression by the reciprocal of the second expression.
3x^3/5y^2÷ 2* 3x^3* x^2/5y^2* y
⇕
3x^3/5y^2* 5y^2* y/2* 3x^3* x^2
Finally, we can cancel out any common factors.
To identify the restrictions on the variables, we need to find any values of x and y that would cause the denominator of the simplified expression, or any other denominator used, to be 0.
Denominator
Restrictions on the denominator
Restrictions on the variables
5y^2
5y^2≠ 0
y≠ 0
5x^(-5)
x^5≠ 0
x≠ 0
5y^2* y
y^2≠ 0 and y≠0
y≠ 0 and y≠ 0
2* 3x^3* x^2
3x^3≠ 0 and x^2≠ 0
x≠ 0 and x≠ 0
2x^2
2x^2≠ 0
x≠ 0
We found two restrictions on the variables.
y≠ 0, x≠ 0
