NBT NBT Mathematics: Exponents, Surds and Equations 1 — Questions and Answers
Question 1: Simplify: $2^{3} \times 2^{-5}$
- $2^{-2}$ (Correct answer)
- $2^{2}$
- $2^{8}$
- $2^{-8}$
Correct answer: $2^{-2}$
When multiplying powers with the same base, add the exponents: $3 + (-5) = -2$, giving $2^{-2}$.
Question 2: Which of the following is equal to $\sqrt{75}$?
- $5\sqrt{3}$ (Correct answer)
- $3\sqrt{5}$
- $15\sqrt{3}$
- $25\sqrt{3}$
Correct answer: $5\sqrt{3}$
$\sqrt{75} = \sqrt{25 \times 3} = 5\sqrt{3}$.
Question 3: Solve for $x$: $3^x = 81$
- $x = 4$ (Correct answer)
- $x = 3$
- $x = 27$
- $x = 9$
Correct answer: $x = 4$
$81 = 3^4$, so $x = 4$.
Question 4: Rationalise the denominator: $\dfrac{6}{\sqrt{3}}$
- $2\sqrt{3}$ (Correct answer)
- $3\sqrt{2}$
- $6\sqrt{3}$
- $\dfrac{6}{3}$
Correct answer: $2\sqrt{3}$
$\dfrac{6}{\sqrt{3}} \times \dfrac{\sqrt{3}}{\sqrt{3}} = \dfrac{6\sqrt{3}}{3} = 2\sqrt{3}$.
Question 5: Simplify: $\dfrac{x^6}{x^{-2}}$
- $x^8$ (Correct answer)
- $x^4$
- $x^3$
- $x^{-12}$
Correct answer: $x^8$
Dividing powers with the same base: $6 - (-2) = 8$, giving $x^8$.
Question 6: Solve for $x$: $x^2 - 5x + 6 = 0$
- $x = 2$ or $x = 3$ (Correct answer)
- $x = -2$ or $x = -3$
- $x = 1$ or $x = 6$
- $x = 2$ or $x = -3$
Correct answer: $x = 2$ or $x = 3$
Factorising: $(x-2)(x-3) = 0$, so $x = 2$ or $x = 3$.
Question 7: Which expression is equal to $(27)^{2/3}$?
- $9$ (Correct answer)
- $18$
- $3$
- $6$
Correct answer: $9$
$(27)^{2/3} = (\sqrt[3]{27})^2 = 3^2 = 9$.
NBT NBT Mathematics: Exponents, Surds and Equations 1
Simplify: $2^{3} \times 2^{-5}$