Answer:
y^3/2x^4.
Explanation:
To simplify the expression (2x^4y^-3)^-1, we can use the property of negative exponents. When a term with a negative exponent is raised to the power of -1, it essentially becomes its reciprocal.
Let's break down the expression step-by-step:
1. Start with the given expression: (2x^4y^-3)^-1
2. Apply the negative exponent rule:
- The negative exponent rule states that any term with a negative exponent can be rewritten as its reciprocal with the exponent changed to positive.
- In this case, the term y^-3 becomes 1/y^3.
3. Simplify the expression:
(2x^4/y^3)^-1
4. Apply the reciprocal rule:
- When a term is raised to the power of -1, we can rewrite it as its reciprocal with the exponent changed to positive.
- So, (2x^4/y^3)^-1 becomes 1/(2x^4/y^3).
5. Simplify further:
1/(2x^4/y^3)
6. Apply the division rule:
- When dividing fractions, we multiply the first fraction by the reciprocal of the second fraction.
- In this case, we have 1 divided by (2x^4/y^3). This can be rewritten as 1 times (y^3/2x^4).
7. Simplify the expression:
1 * (y^3/2x^4)
y^3/2x^4
So, the simplified expression for (2x^4y^-3)^-1 is y^3/2x^4.