Using indices rules to write powers as negative powers

Writing negative powers as fractions

Writing fractins as negative powers

Using indices rules to write expressions as negative powers.

Using indices rules to write fractions as negative powers.

Using rules for roots and powers to write expressions with only powers

Using indices to write roots as fractional powers

Find the eigenfunctions of an irregular Sturm–Liouville problem and hence solve an inhomogeneous boundary value problem by writing the solution as an eigenfunction expansion.

Rewriting expressions of the form $n\log(a)\pm m\log(b)$ as a single logarithm.

Rewriting $\log_{10}(x)$ in terms of $\log_{10}(a)$ and $\log_{10}(b)$, where $a$, $b$ and $x$ are given.

Solve an ODE by first writing it in canonical form.

Rewriting a trigonometric expression of the form $A\cos(\theta)\pm B\sin(\theta)$ to either $R\sin(\theta+\alpha)$ or $R\cos(\theta+\alpha)$ by calculating $R$ and $\alpha$. 

Rewriting a trigonometric expression of the form $A\sin(\theta)-B\cos(\theta)$ to $R\sin(\theta-\alpha)$ by calculating $R$ and $\alpha$.

Rewriting fractions of the form $\frac{\sqrt[m]{x^n}}{\sqrt[p]{x^q}}$ to $x^{\frac{n}{m}-\frac{q}{p}}$.

Rewriting expressions from $\sqrt[m]{x^n}$ to $x^\frac{n}{m}$.

Multiple choice question. Given a randomised polynomial select the possibe ways of writing the domain of the function.

Multiple choice questions. Given randomised trig functions select the possible ways of writing the domain of the function.

Given a randomised square root function select the possible ways of writing the domain of the function.

Multiple choice question. Given a randomised polynomial select the possibe ways of writing the domain of the function.

Multiple choice question. Given a randomised polynomial select the possibe ways of writing the domain of the function.

Multiple choice question. Given a randomised polynomial select the possible ways of writing the domain of the function.

Given a randomised log function select the possible ways of writing the domain of the function.

Given a randomised rational function select the possible ways of writing the domain of the function.

Rewriting fractions involving surds by rationalising the denominator.

Rewriting fractions involving surds by rationalising the denominator.

Rewriting expressions involving surds into the form $a+b \sqrt{c}$, where $a$, $b$ and $c$ are integers.

Rewriting expressions involving surds into the form $a+b \sqrt{c}$, where $a$, $b$ and $c$ are integers.

Rewriting expressions involving surds into the form $a+b \sqrt{c}$, where $a$, $b$ and $c$ are integers.

Rewriting fractional expressions involving $\sqrt[n]{x^m}$ using rules to combine and simplify indices. 

Writing one number as a percentage of another.