Distance, powers and roots

Easy0 of 22 parts

Every part here is a paper exercise and should stay one. Work it out with a pencil, then type what you wrote. Reaching for a calculator gives a decimal, and a decimal is not what an exam wants.

Evaluate $|3 - 11|$ .

Write the distance between $x$ and $-4$ as an expression in $x$ .

in terms of x

Evaluate $\sqrt{(-6)^{2}}$ .

Simplify $\dfrac{\left(2x^{3}\right)^{4}}{4x^{5}}$ , taking $x$ to be positive.

in terms of x

Simplify $\left(\dfrac{3x^{-2}}{y^{3}}\right)^{-2}$ , taking $x$ and $y$ to be positive.

in terms of x, y

Evaluate $16^{-3/4}$ .

Evaluate $\left(\dfrac{8}{125}\right)^{-2/3}$ .

Write $\dfrac{1}{x^{2}\sqrt[3]{x}}$ as a single power of $x$ , for $x > 0$ .

in terms of x

Simplify $\sqrt{48x^{7}}$ , taking $x$ to be positive.

in terms of x

Rationalise the denominator of $\dfrac{5}{\sqrt{10}}$ .

Evaluate $|2.4 - 7.1|$ .

Simplify $\left(\dfrac{x^{-3}y^{2}}{2x^{2}}\right)^{-1}$ , taking $x$ and $y$ to be positive.

in terms of x, y

The number $0.00000903$ is written in scientific notation as $a \times 10^{n}$ , with $1 \le a < 10$ . What is $n$ ?

Work out $(6 \times 10^{8}) \div (1.5 \times 10^{-3})$ , and give the answer in scientific notation.

Work out $(2.5 \times 10^{-4})(8 \times 10^{7})$ , and give the answer in scientific notation.

Simplify $\sqrt[3]{80}$ .

Simplify $\sqrt[3]{54x^{5}}$ , taking $x$ to be positive.

in terms of x

Simplify $\sqrt{75}+\sqrt{12}$ .

Simplify $2\sqrt{27}-\sqrt{48}$ .

Simplify $\sqrt{45}+\sqrt{80}$ .

Rationalise the denominator of $\dfrac{4}{\sqrt{7}-\sqrt{3}}$ .

Rationalise the denominator of $\dfrac{3}{2+\sqrt{5}}$ .