Question

Simplify the expression using the properties of exponents. Expand any numerical portion of your answer and only include positive exponents.

(3x2/y−1)3

Answer 1

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