Question

Simplify using the rules for exponents. Use only positive exponents in your answer. ((6x-⁴y⁷)/(18x²y-⁸))-²

Answer 1

To simplify the expression ((6x^-4y^7)/(18x^2y^-8))^-2, divide the numerator and denominator separately, simplify the exponents, rewrite the expression with positive exponents, and apply the power rule for exponents.

Step-by-step explanation:

To simplify the expression ((6x-4y7)/(18x2y-8))-2, we need to apply the rules for exponents. Here are the steps:

1. Divide the numerator and denominator separately:
2. (6x-4y7)/(18x2y-8) = (6/18)x-4-2y7-(-8)
3. Simplify the numerator and denominator:
4. (1/3)x-6y15
5. Rewrite the expression with positive exponents:
6. 1/(3x6y-15)
7. Apply the power rule for exponents:
8. (3x6y-15)-2 = 3-2x6(-2)y-15(-2) = 1/(32x-12y30)