Simplify the expression using the properties of exponents. Expand any numerical portion of your answer and only include positive exponents.
(3x2/y−1)3
To simplify the expression, we can apply the property of exponents that states that when a power is raised to another power, we multiply the exponents.
So, we have:
(3x^2/y^(-1))^3
Expanding the power, we have:
(3^3 * (x^2)^3 / (y^(-1))^3)
Simplifying further, we have:
(27 * x^(2*3) / y^(-1*3))
This simplifies to:
(27 * x^6 / y^(-3))
Finally, using the property of exponents that states that a negative exponent is equivalent to the reciprocal of the number with a positive exponent, we can rewrite y^(-3) as 1/y^3:
(27 * x^6 / (1/y^3))
Applying the property of division of fractions, we can multiply the numerator by the reciprocal of the denominator:
27x^6y^3