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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. v^{7} \times v^{3}
  2. p^{11} \times p^{8}
  3. u^{6} \times u^{14}
  4. q^{-2} \times q^{-8}
  5. v^{7} \div v^{3}
  6. p^{11} \div p^{8}
  7. u^{6} \div u^{14}
  8. q^{-2} \div q^{-8}
  9. \left( v^{7} \right)^{3}
  10. \left( p^{11} \right)^{8}
  11. \left( u^{6} \right)^{14}
  12. \left( q^{-2} \right)^{-8}

    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^{5}
  14. \left( 2^{3} \right)^{4}
  15. 5^{8} \times 5^{-6}
  16. 1^{35} \times 1^{49}

    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( 3v^{3} \right)^{2}
  19. \left( 3t^{2} \right)^{3}