University:
Carleton College
Course:
MATH 120 | Calculus 2
Academic year:

2024
Views:

474

Pages:

2
Author:

Nevaeh Bauer

Question 1 To calculate: To convert the radical expression ³√(x⁶y⁹) to rational exponent form and simplify. Answer Calculation: According to exponential rules, ⁿ√a = a^(1/n) Given ³√(x⁶y⁹) Applying the above rule: where a = x⁶y⁹ , n = 3 ³√(x⁶y⁹) = (x⁶y⁹)^(1/3) According to product rule, (ab)ⁿ = aⁿ * bⁿ Applying the above rule: where a = x⁶, b = y⁹, n = 1/3 ³√(x⁶y⁹) = (x⁶)^(1/3) (y⁹)^(1/3) According to the power rule, (aᵐ)ⁿ = aᵐⁿ Applying the above rule: ³√(x⁶y⁹) = x^(6*(1/3)) y^(9*(1/3)) ³√(x⁶y⁹) = x²y³ Question 2 To calculate the radical expression ³√(x¹²) to rational exponent form and simplify. Answer Calculation: According to exponential rules, ⁿ√a = a^(1/n) Given ³√(x¹²) Applying the above rule: where a = x¹², n = 3 ³√(x¹²) = (x¹²)^(1/3) According to the power rule, (aᵐ)ⁿ = aᵐⁿ Applying the above rule: where a = x, m = 12, n = 1/3 ³√(x¹²) = x^(12*(1/3)) ³√(x¹²) = x⁴. Question 3 Rewrite the rational exponent as a radical by extending the properties of integer 7/8 exponents. 2^(7/8) divided by 2^(1/4) Answer b/c We know the rule of change: a = (ac+b):c So we have 2^(7/8) = (2 x 8 + 7) / 8 = 23/8 and the second: 2^(1/4) = (2 x 4 + 1) / 4 = 9/4 We do the division: 23/8 ÷ 9/4 = 23/8 * 4/9 = (23 * 4) / (8 * 9) = 92 / 72 = 23 / 18 = 1 5/18