BC Math 9 Exponents

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Learning Outcomes

• Exponents and Exponent laws with whole-number exponents
• Includes variable bases
• 2^7=2\times2\times2\times2\times2\times2\times2=128;
  n^4=n\times n\times n\times n
• Exponent laws ex. 6^0=1; m^1=m; n^5\times n^3=n^8; \frac{y^7}{y^3}=y^4;
  (5n)^3=5^3\times n^3; \left(\frac{m}{n}\right)^5=\frac{m^5}{n^5}; and \left(3^2\right)^4=3^8
• Limited to whole-number exponents and whole-number exponent outcomes when simplified
• (-3)^2 does not equal -3^2
  

Lesson Examples

1. 2^6
   Solution
   64
2. 3^4
   Solution
   81
3. Simplify a\times a\times a\times a\times a
   Solution
   a^5
4. (-3)^4
   Solution
   81
5. n\times n^7\times n^4
   Solution
   n^{12}
6. \left(x^5\right)(x)\cdot x^3
   Solution
   x^9
7. \left(3x^3\right)^3
   Solution
   27x^9
8. \left(\frac{2}{-3}\right)^3
   Solution
   -\frac{8}{27}
9. Simplify \frac{x^5}{x^3}
   Solution
   x^2
10. x^a\cdot x^b
    Solution
    x^{a+b}
11. \left(\frac{2}{3}\right)^3
    Solution
    \frac{8}{27}
12. \left(\frac{a}{b}\right)^c
    Solution
    \frac{a^c}{b^c}
13. Evaluate -5^2
    Solution
    -25
14. Evaluate (-5)^2
    Solution
    25
15. \frac{x^5}{x^3}\div \frac{x}{x^2}
    Solution
    x^3
16. \frac{5ab^3c}{15a^3b^5}
    Solution
    \frac{c}{3a^2b^2}
17. \left(x^2\right)^3
    Solution
    x^6
18. \left(a^b\right)^c
    Solution
    a^{bc}
19. \left( \frac{2x^2y^3}{z^5} \right) ^3
    Solution
    \frac{8x^6y^9}{z^{15}}
20. \frac{(-3)^4}{(-3)^2}\times -3^2
    Solution
    -81
21. -2(-2)^2-(-3)^2
    Solution
    -17
22. \left(\left(2x^2\right)^3\right)^2
    Solution
    64x^{12}
23. \left(2\left(3a^2\right)^3\right)^2
    Solution
    2916a^{12}
24. (-1)^{2024}
    Solution
    1
25. \frac{(-2)^{100}}{-2^{98}}
    Solution
    -4
26. 1^0+0^1
    Solution
    1
27. 0^0
    Solution
    Undefined
28. \left(\frac{4p^4p^6q^4}{2p^8q^3}\right)^3
    Solution
    8p^6q^3
29. \left(\frac{(-3)^2}{(-2)^4}\right)^2
    Solution
    \frac{81}{256}
30. -2\left(-\frac{3}{4}\right)^2+(-1)^3-\left(\frac{-2^4}{(-2)^3}\right)^2
    Solution
    -\frac{49}{8}
31. \frac{2}{x}\left(\frac{3x}{2x^2}\right)^3\div \frac{1}{x^3}
    Solution
    \frac{27}{4x}
32. Solve 27=9^{3x}
    Solution
    x=\frac{1}{2}
33. Solve \frac{3^{10}}{3^x}=3^{x+1}
    Solution
    x=\frac{9}{2}
34. Solve 8^{1-2x}=\frac{2^9}{2^x}
    Solution
    x=-\frac{6}{5}
35. Challenge:
    1. \left[\frac{(-3^3)}{3^2}\right]^2-\left[\frac{(-3)^4}{3^3}\right]^1+\left[\frac{(-3)^1}{3}\right]^0
       Solution
       7
    2. \left(\frac{8^{1-2x}}{2^{x+3}}\right)^4=2
       Solution
       x=-\frac{1}{28}
    3. Solve 32\times 2+2^{x+1}=3\times 2^x
       Solution
       x=6

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