Question

Simplify The Following Expression So All Exponents Are Positive. ((8x^(-4)Y^(-2))/(2x^(3)Y^(-4)))^(-1)

Answer 1

To simplify the expression and make all exponents positive, we apply the rules of exponents.

Step-by-step explanation:

To simplify the expression and make all exponents positive, we will need to apply the rules of exponents:

1. Reciprocal of a fraction: When a fraction is raised to a negative power, we can find its reciprocal and change the sign of the exponent.
2. Power of a product: When a product is raised to an exponent, we can apply the exponent to each term inside the parentheses.
3. Power of a power: If a power is raised to another power, we can multiply the exponents together.

Let's apply these rules to the given expression:

((8x^(-4)Y^(-2))/(2x^(3)Y^(-4)))^(-1)

1. Apply the reciprocal: ((2x^(3)Y^(-4))/(8x^(-4)Y^(-2)))
2. Apply the power of a product: (2x^(3-(-4))Y^(-4-(-2)))
3. Simplify the exponents: (2x^(7)Y^(-2))

Therefore, the simplified expression with all exponents positive is 2x^(7)Y^(-2).

Learn more about Simplifying expressions