OpenRevise

Flashcards · Maths · Number Without a Calculator

Powers, Roots and Indices

19 cards

  1. What does \(a^n\) mean?

    \(a\) multiplied by itself \(n\) times, so \(2^5 = 32\).

  2. Which square numbers should you know up to \(15^2\)?

    1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196 and 225.

  3. Which cube numbers should you know?

    1, 8, 27, 64, 125 and \(10^3 = 1000\).

  4. What is \(\sqrt{196}\)?

    14.

  5. Is \(4^3\) equal to 12?

    No. \(4^3 = 4 \times 4 \times 4 = 64\).

  6. What is the law for \(a^m \times a^n\)?

    Add the indices: \(a^{m+n}\).

  7. What is the law for \(a^m \div a^n\)?

    Subtract the indices: \(a^{m-n}\).

  8. What is the law for \((a^m)^n\)?

    Multiply the indices: \(a^{mn}\).

  9. Can the index laws simplify \(2^3 \times 5^2\)?

    No, because the bases are different. Work out each power instead: \(8 \times 25 = 200\).

  10. What is \(a^0\)?

    1, for any non-zero \(a\).

  11. What is \(5^{-2}\)?

    \(\dfrac{1}{25}\). A negative index means a reciprocal, not a negative number.

  12. What is \(\left(\dfrac{2}{3}\right)^{-2}\)?

    Flip the fraction, then square: \(\left(\dfrac{3}{2}\right)^2 = \dfrac{9}{4}\).

  13. What is \(49^{\frac{1}{2}}\) (Higher tier)?

    The square root of 49, which is 7.

  14. What is \(8^{\frac{2}{3}}\) (Higher tier)?

    Take the cube root first, then square: \(2^2 = 4\).

  15. Between which two whole numbers does \(\sqrt{40}\) lie?

    6 and 7, because \(36 < 40 < 49\).

  16. How do you write \(16 \times 8\) as a single power of 2?

    \(2^4 \times 2^3 = 2^7\).

  17. What is \(10^{-3}\) as a decimal?

    0.001.

  18. What is the mistake in \(3^2 \times 3^4 = 9^6\)?

    Add the indices and keep the base: \(3^2 \times 3^4 = 3^6\).

  19. What is \((2x)^2\)?

    \(4x^2\). The 2 is squared as well.