[login]
QMMaths

Rules of indices

Stuck? Read the notes

Answers

To enter an answer such as p^{12}, type p^12 in the answer box.

    Simplify the following, using the rules of indices.

  1. y^{7} \times y^{2}
  2. s^{8} \times s^{5}
  3. p^{5} \times p^{12}
  4. w^{-3} \times w^{-5}
  5. y^{7} \div y^{2}
  6. s^{8} \div s^{5}
  7. p^{5} \div p^{12}
  8. w^{-3} \div w^{-5}
  9. \left( y^{7} \right)^{2}
  10. \left( s^{8} \right)^{5}
  11. \left( p^{5} \right)^{12}
  12. \left( w^{-3} \right)^{-5}

    13. Use the rules of indices to simplify the following and then to work out the answer as an ordinary number, without a calculator.

  13. 3^{9} \div 3^{6}
  14. \left( 2^{2} \right)^{3}
  15. 5^{7} \times 5^{-5}
  16. 1^{58} \times 1^{45}

    17. The expression (2x^3)^2 does not simplify to 2x^6 as it is equal to 2x^3\times 2x^3

  17. What does it simplify to?

    18. Using the same reasoning, simplify

  18. \left( 2z^{3} \right)^{2}
  19. \left( 3u^{2} \right)^{3}