Check Your Skills Answer Key

1. (−5)⁸: −5⁸ = −1 × 5⁸, and is thus negative. (−5)⁸ will be positive, since the exponent is even. A positive is always greater than a negative.

2. b¹²: The bases are the same, so add the exponents.

   

3. x⁷: The bases are the same, so add the exponents.

   

4. y³: The bases are the same, so subtract the bottom exponent from the top exponent.

   

5. d or d¹: The bases are the same, so subtract the bottom exponent from the top exponent. d¹ is more commonly written d.

   

6. :
   
7. 27:

   

8. x¹²:

   = x^{3 × 4} = x¹²

9. a⁶:

   

10. x⁴y²z⁶:

    

11. 15:

    

12. 5³(5² + 5 − 1) or 5³(29):
    5⁵ + 5⁴ − 5³ = 5³(5² + 5¹ − 1) = 5³(25 + 5 − 1) = 5³(29)

13. 27: Any square root times itself equals the number underneath the square root symbol.

14. x³: Since x is positive, x³ is positive, too.
    

15. 16:

    

    You could also square the 64 first, but that would be very annoying math to do without a calculator.

16. 10:

    

17. 6:

    

    Simplify before you multiply!

18. :
    
19. 15: Did you recognize this root? This is one of the common ones; if you have it memorized, you don’t have to do any work at all! The square root of 225 is 15. Here’s the math:

    

20. 300: