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QMMaths

Rules of indices

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

    Simplify the following, using the rules of indices.

  1. u^{7} \times u^{2}
  2. t^{12} \times t^{8}
  3. x^{2} \times x^{13}
  4. s^{-3} \times s^{-7}
  5. u^{7} \div u^{2}
  6. t^{12} \div t^{8}
  7. x^{2} \div x^{13}
  8. s^{-3} \div s^{-7}
  9. \left( u^{7} \right)^{2}
  10. \left( t^{12} \right)^{8}
  11. \left( x^{2} \right)^{13}
  12. \left( s^{-3} \right)^{-7}

    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^{6} \div 3^{4}
  14. \left( 2^{2} \right)^{4}
  15. 5^{6} \times 5^{-5}
  16. 1^{38} \times 1^{31}

    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( 4x^{3} \right)^{2}
  19. \left( 4y^{2} \right)^{3}