Technical Mathematics, Sixth Edition

13.5. CHAPTER 13 REVIEW PROBLEMS

Simplify. Don't use a calculator.

Perform the indicated operations and simplify. Don't use a calculator.

Solve for x and check:

Simplify, and write without negative exponents.

1. (xⁿ⁻¹ + yⁿ⁻²)(xⁿ + yⁿ⁻¹)

2. (72a⁶b⁷ ÷ 9a⁴b) ÷ 8ab⁶ a

   33. x²ⁿ⁻¹ + (xy)ⁿ⁻¹ + xⁿyⁿ⁻² + y²ⁿ⁻³

3. 

4. 

5. 

6. 5a⁻¹ 5/a

7. 3w⁻² 3/w²

8. 2r⁰ 2

9. (3x)⁻¹ 1/(3x)

10. 2a⁻¹ + b⁻² 2/a + 1/b²

11. x⁻¹ − 2y⁻² 1/x − 2/y²

12. (5a)⁻³ − 3b⁻² 1/(125a³ − 3/b²)

13. (3x)⁻² + (2x²y⁻⁴)⁻²

    45. 1/(9x²) + y⁸/(4x⁴)

    46. a²ⁿ + 2aⁿb^m + b²m

    47. p^2a−1 + (pq)^a−1 + p^aq^a−2 + q^2a−3

    48. a/(2b⁷)

14. (aⁿ + b^m)²

15. (p^a−1 + q^a−2)(p^a + q^a−1)

16. (16a⁶b⁰ ÷ 8a⁴b) ÷ 4ab⁶

17. p²q⁻¹ p²/q

18. x³y⁻² x³/y²

19. r²s⁻³ r²/s³

20. x³y⁻² x³/y²

21. (3x³y²z)⁰ 1

22. (5a²b²c²)³ 125(abc)⁶

23. The volume V of a sphere of radius r is given

    

    If the radius is tripled, the volume is then

    Simplify this expression. V = 36πr³

24. Find the missing side and the hypotenuse ...