Question

(5xy^3/x^4y)^-2

Answer 1

[AI-generated answer — Explain Bot]

To simplify the expression (5xy^3/x^4y)^-2, you can follow these steps:

Step 1: Start by applying the negative exponent to the entire fraction by flipping the numerator and denominator. This is because a negative exponent indicates that the base should be moved to the opposite position in the fraction.

So, (5xy^3/x^4y)^-2 becomes (x^4y/5xy^3)^2.

Step 2: Simplify the expression within the parentheses. To do this, divide the common factors and subtract the exponents.

In this case, the common factors between the numerator and denominator are x and y^3. The exponent of x in the numerator is 4, and the exponent of x in the denominator is 1. So, x^4/x^1 reduces to x^(4-1), which is x^3.

Similarly, the exponent of y in the numerator is 1, and the exponent of y in the denominator is 3. So, y^1/y^3 reduces to y^(1-3), which is y^(-2).

Combining these results, we have x^3/y^2.

Step 3: Apply the exponent of 2 to each factor within the fraction.

(x^3/y^2)^2 becomes x^3^2 / y^2^2, which simplifies to x^6 / y^4.

Therefore, the simplified expression for (5xy^3/x^4y)^-2 is x^6 / y^4.