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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. Which of the following equals $16^{-3/4}$?

    Answer: $\dfrac{1}{8}$

    $16^{3/4} = (\sqrt[4]{16})^3 = 2^3 = 8$, so $16^{-3/4} = \dfrac{1}{8}$.

  2. Solve: $\sqrt{2x + 3} = 5$

    Answer: $x = 11$

    Squaring both sides: $2x + 3 = 25$, so $x = 11$.

  3. Simplify: $2^{10} \div 2^{7}$

    Answer: $8$

    $2^{10-7} = 2^3 = 8$.

  4. Expand and simplify: $(\sqrt{5} + \sqrt{2})(\sqrt{5} - \sqrt{2})$

    Answer: $3$

    Using difference of squares: $(\sqrt{5})^2 - (\sqrt{2})^2 = 5 - 2 = 3$.

  5. Solve for $x$: $x^2 - 7x = 0$

    Answer: $x = 0$ or $x = 7$

    Factorising: $x(x-7) = 0$, so $x = 0$ or $x = 7$.

  6. What is the value of $x$ if $4^x = \dfrac{1}{16}$?

    Answer: $x = -2$

    $\dfrac{1}{16} = 4^{-2}$, so $x = -2$.

  7. Simplify: $\dfrac{\sqrt{50}}{\sqrt{2}}$

    Answer: $5$

    $\dfrac{\sqrt{50}}{\sqrt{2}} = \sqrt{\dfrac{50}{2}} = \sqrt{25} = 5$.