NBT NBT Mathematics: Exponents, Surds and Equations 3 — Questions and Answers
Question 1: Which of the following equals $16^{-3/4}$?
- $\dfrac{1}{8}$ (Correct answer)
- $8$
- $\dfrac{1}{4}$
- $4$
Correct answer: $\dfrac{1}{8}$
$16^{3/4} = (\sqrt[4]{16})^3 = 2^3 = 8$, so $16^{-3/4} = \dfrac{1}{8}$.
Question 2: Solve: $\sqrt{2x + 3} = 5$
- $x = 11$ (Correct answer)
- $x = 14$
- $x = 7$
- $x = 22$
Correct answer: $x = 11$
Squaring both sides: $2x + 3 = 25$, so $x = 11$.
Question 3: Simplify: $2^{10} \div 2^{7}$
- $8$ (Correct answer)
- $4$
- $16$
- $2$
Correct answer: $8$
$2^{10-7} = 2^3 = 8$.
Question 4: Expand and simplify: $(\sqrt{5} + \sqrt{2})(\sqrt{5} - \sqrt{2})$
- $3$ (Correct answer)
- $7$
- $\sqrt{3}$
- $5\sqrt{2}$
Correct answer: $3$
Using difference of squares: $(\sqrt{5})^2 - (\sqrt{2})^2 = 5 - 2 = 3$.
Question 5: Solve for $x$: $x^2 - 7x = 0$
- $x = 0$ or $x = 7$ (Correct answer)
- $x = 7$ only
- $x = 0$ only
- $x = -7$ or $x = 0$
Correct answer: $x = 0$ or $x = 7$
Factorising: $x(x-7) = 0$, so $x = 0$ or $x = 7$.
Question 6: What is the value of $x$ if $4^x = \dfrac{1}{16}$?
- $x = -2$ (Correct answer)
- $x = 2$
- $x = -4$
- $x = 4$
Correct answer: $x = -2$
$\dfrac{1}{16} = 4^{-2}$, so $x = -2$.
Question 7: Simplify: $\dfrac{\sqrt{50}}{\sqrt{2}}$
- $5$ (Correct answer)
- $10$
- $5\sqrt{2}$
- $\sqrt{25}$
Correct answer: $5$
$\dfrac{\sqrt{50}}{\sqrt{2}} = \sqrt{\dfrac{50}{2}} = \sqrt{25} = 5$.
NBT NBT Mathematics: Exponents, Surds and Equations 3
Which of the following equals $16^{-3/4}$?