Simplify the following expression.
Start Fraction negative 24 x superscript 4 baseline y cubed over 8 x superscript 6 baseline y squared End Fraction
(1 point)
Responses
negative 3 x squared y
Image with alt text: negative 3 x squared y
Start Fraction negative 3 y over x squared End Fraction
Image with alt text: Start Fraction negative 3 y over x squared End Fraction
Start Fraction negative 3 x squared over y End Fraction
Image with alt text: Start Fraction negative 3 x squared over y End Fraction
Start Fraction negative 3 over x squared y End Fraction
The correct simplified expression is Start Fraction negative 3 x squared over y End Fraction.
To simplify the expression
Start Fraction negative 24 x^4 y^3 over 8 x^6 y^2 End Fraction,
we can simplify the numerator and denominator separately.
In the numerator, we divide each exponent by the common factor of 4:
x^4 = x^(4/4) = x^1 = x,
y^3 = y^(3/4) = y^(3/4).
Therefore, the simplified numerator is x * y^(3/4).
In the denominator, we divide each exponent by the common factor of 2:
x^6 = x^(6/2) = x^3,
y^2 = y^(2/2) = y^1 = y.
Therefore, the simplified denominator is x^3 * y.
Putting it all together, the simplified expression is:
Start Fraction negative 24 x^4 y^3 over 8 x^6 y^2 End Fraction = Start Fraction negative 3 x * y^(3/4) over x^3 * y End Fraction.
This can also be written as:
Start Fraction negative 3 y over x^2 End Fraction.