NBT NBT Mathematics: Exponents, Surds and Equations 1

Question 1

Simplify: $2^{3} 	imes 2^{-5}$

Accepted Answer

$2^{-2}$

Answer

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 $\sqrt{75}$?

Accepted Answer

$5\sqrt{3}$

Answer

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

Question 3

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

Accepted Answer

$x = 4$

Answer

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

Question 4

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

Accepted Answer

$2\sqrt{3}$

Answer

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

Question 5

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

Accepted Answer

$x^8$

Answer

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

(NBT) National Benchmark Test Practice Test