simplify 4xy^-2/((12x^-1/3)(y^-5))
4xy^(-2)/((12x^(-1)/3)(y^(-5)))
=4(x/y²)/(12/(3xy^5))
=(4/12)(3x*xy^5)/y²
=x²y³
To simplify the expression 4xy^-2/((12x^-1/3)(y^-5)), we can start by simplifying the numerator and the denominator separately, and then combine the simplified terms.
Let's start with the numerator: 4xy^-2.
The variable x does not have any exponent, so we can write it as x^1.
Now, the variable y has an exponent of -2. To simplify it, we can use the rule that says a negative exponent can be written as the reciprocal of the positive exponent. In this case, y^-2 can be written as 1/y^2.
So, the numerator simplifies to 4x/y^2.
Moving on to the denominator: (12x^-1/3)(y^-5).
The variable x has an exponent of -1/3. To simplify it, we can use the rule that says a fractional exponent represents a root. In this case, x^-1/3 represents the cube root of x to the power of -1.
Similarly, the variable y has an exponent of -5. So, we can write y^-5 as 1/y^5.
Now, the denominator becomes (12∛x)(1/y^5).
To simplify the entire expression, we can multiply the numerator by the reciprocal of the denominator.
4x/y^2 / (12∛x)(1/y^5) can be rewritten as (4x/y^2) * (y^5/(12∛x)).
Now, let's simplify further:
(4x * y^5) / (y^2 * 12∛x)
We can cancel out the y^2 terms:
(4x * y^5) / (12∛x)
Finally, we simplify the expression by dividing both the numerator and denominator by the greatest common factor, which is 4:
y^5 / (3∛x)
Therefore, the simplified expression is y^5 / (3∛x).