The expression
(16xy^2/-24x^3y)^-3
may be simplified into the form A/B
where none of the factors of A and B are raised to a negative power.
Answer: A = _______ and B = ________
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Here it's probably best to simplfy inside the parens first:
16xy^2/-24x^3y = -2y/3x^2
Now raise that to the -3 power:
(-2y/3x^2)^-3
= (-3x^2/2y)^3
= ((-3)^3 (x^2)^3 / (2^3) (y^3)
= -27x^6 / 8y^3
A = -24y^6x^9
B = 16y^2x^3
To simplify the expression (16xy^2/-24x^3y)^-3, we can start by simplifying the numerator and denominator separately.
Numerator:
16xy^2
Denominator:
-24x^3y
Now let's simplify the expression inside the parentheses (-3 exponent):
Numerator:
(16xy^2)^-3 = 1/(16xy^2)^3 = 1/(16^3 * x^3 * (y^2)^3) = 1/(4096x^3y^6)
Denominator:
(-24x^3y)^-3 = 1/(-24x^3y)^3 = 1/(-24^3 * x^3 * y^3) = 1/(-13824x^3y^3)
Therefore, the simplified form of the expression is:
A = 1
B = -13824x^3y^3 / 4096x^3y^6
To simplify the expression (16xy^2/-24x^3y)^-3, we can start by combining the numerator and denominator.
The numerator is 16xy^2, and the denominator is -24x^3y.
Next, we raise this fraction to the power of -3.
When we have a negative exponent, we can move it to the opposite position in the fraction by taking its reciprocal. So, the expression becomes (-24x^3y/16xy^2)^3.
Now, let's simplify the fraction part (-24x^3y/16xy^2).
We can start by canceling out common factors between the numerator and the denominator. In this case, we can cancel out a factor of 8, x, and y.
After canceling, we get -3x^2/2y.
Now, we need to raise this simplified fraction (-3x^2/2y) to the power of 3.
To do that, we can raise the numerator and the denominator to the power of 3 individually.
The numerator raised to the power of 3 becomes (-3)^3 * (x^2)^3 = -27x^6.
The denominator raised to the power of 3 becomes (2)^3 * (y)^3 = 8y^3.
So, the simplified expression is (-27x^6/8y^3).
Therefore, A = -27x^6 and B = 8y^3.