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Exponents

Worksheet

Try each of the 24 questions below. If you need help, click on the question marks to see solutions worked out step-by-step.

 

Write the following in abbrieviated form using exponents:

  1. 4*4*4*4*4*4*4= 4^7
  2. y*y*y*y=y^4
  3. y*z*y*x*x*z*x*y=x^3*y^3*z^2

  4. The third root of 27 =3
  5. The fifth power of 321.55 to 2 dp


    Write the following in abbreviated form using negative exponents:

  6. 1/7*1/7*1/7*1/7*1/7=7^(-5)

  7. 1/a*1/b*1/b*1/a*1/b*1/b=a^(-2)*b^(-4)



    Evaluate:

  8. 3^5=243

  9. 2^(-4)=0.0625

  10. 27^(-1/3)=1/27^(1/3)=1/3

  11. (1/9)^(5/2) =(1/3)^5=1/243
  12. 2.5^(-1.7)= 0.21 to 2dp



    Simplify as far as you can:

  13. a^5*a^3= a^8

  14. x^2*x^4*x^7*x^3 =x^16

  15. x^4*y^4*x^2*z^3*y^2*z*x^7 =x^13*y^6*x^4

  16. a^2/a^7=a^-5

  17. (2*a^4*b)/(6*a*b^2) =a^3/(3b)

  18. (z^5)^3 =z^15

  19. (3*a^3*b^7)^2 =9*a^6*b^14

  20. (a^8)^4/(a^3)^2 =a^32/a^6=a26

  21. (w^3*x^(-2)*z^(-5))/(w^(-3)*z^2)^(-4)=(w^3*x^(-2)*z^(-5))/(w^12*z^-8)=z^3/(w^9*x^2)

  22. (a^(3/2)*b^(3/4))^16= a^24*b^12

  23. (9*a^6*b^4)^(1/2)=3*a^3*b^2

  24. (3*a^(-2)*b^15*c^(-5))/(a^(-4)*b^3*c)^(-5) = (3*a^(-2)*b^15*c^(-5))/(a^20*b^(-15)*c^(-5)) = (3*b^30)/a^22



 

Exponents Index
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