Question

Which expression is equivalent to (4x−3y4)−2?

negative quantity 16 times x raised to the sixth power end quantity over y raised to the eighth power
−16x6y8
1 over quantity 16 times x raised to the sixth power times y raised to the eighth power end quantity
x raised to the sixth power over quantity 16 times y raised to the eighth power end quantity

Answer 1

The expression (4x−3y4)−2 can be simplified to 1/(16x²−6xy⁴+y⁸).

Step-by-step explanation:

The expression (4x−3y4)−2 can be simplified using the negative exponent rule. When a term with a negative exponent is raised to a negative power, the result is the reciprocal of the term raised to the positive power.

So, (4x−3y4)−2 = 1/(4x−3y4)²

Simplifying further, we get (4x−3y4)−2 = 1/(16x²−6xy⁴+y⁸)

Answer 2

1 over quantity 16 times x raised to the second power minus 48xy raised to the fourth power plus 9y raised to the eighth power end quantity.

Step-by-step explanation:

1. (4x - 3y^4)^-2

2. To simplify the expression, we need to take the reciprocal and apply the exponent to each term inside the parentheses.

3. Taking the reciprocal gives us 1/(4x - 3y^4)^2.

4. Now, let's expand the square of the expression inside the parentheses.

5. (4x - 3y^4)^2 means (4x - 3y^4) * (4x - 3y^4).

6. Expanding, we have 16x^2 - 24xy^4 - 24xy^4 + 9y^8.

7. Simplifying further, we get 16x^2 - 48xy^4 + 9y^8.

8. Now, we can rewrite our expression as 1/(16x^2 - 48xy^4 + 9y^8).