Practice Test Geeks(NBT) National Benchmark Test Practice Test
← All NBT Flashcard Decks

NBT Mathematics: Exponents, Surds and Equations Flashcards

7 cards from real NBT practice questions. Tap to flip, then mark Knew It or Still Learning — missed cards come back until you master them.

Read the first 7 NBT Mathematics: Exponents, Surds and Equations flashcards as text

  1. Simplify: $2^{3} \times 2^{-5}$

    Answer: $2^{-2}$

    When multiplying powers with the same base, add the exponents: $3 + (-5) = -2$, giving $2^{-2}$.

  2. Which of the following is equal to $\sqrt{75}$?

    Answer: $5\sqrt{3}$

    $\sqrt{75} = \sqrt{25 \times 3} = 5\sqrt{3}$.

  3. Solve for $x$: $3^x = 81$

    Answer: $x = 4$

    $81 = 3^4$, so $x = 4$.

  4. Rationalise the denominator: $\dfrac{6}{\sqrt{3}}$

    Answer: $2\sqrt{3}$

    $\dfrac{6}{\sqrt{3}} \times \dfrac{\sqrt{3}}{\sqrt{3}} = \dfrac{6\sqrt{3}}{3} = 2\sqrt{3}$.

  5. Simplify: $\dfrac{x^6}{x^{-2}}$

    Answer: $x^8$

    Dividing powers with the same base: $6 - (-2) = 8$, giving $x^8$.

  6. Solve for $x$: $x^2 - 5x + 6 = 0$

    Answer: $x = 2$ or $x = 3$

    Factorising: $(x-2)(x-3) = 0$, so $x = 2$ or $x = 3$.

  7. Which expression is equal to $(27)^{2/3}$?

    Answer: $9$

    $(27)^{2/3} = (\sqrt[3]{27})^2 = 3^2 = 9$.