Using indices rules to write fractions as negative powers.

Calculate an answer involving a fractional index.

Calculate an answer involving a fractional index.

Calculate an answer involving a fractional index.

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

Using indices to write roots as fractional powers

Using indices rules to rewrite an expression from $a^\frac{m}{n}$ to $b$, for integers $a$, $b$, $m$ and $n$.

Calculate an answer involving a fractional index.

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Simplifying expressions from $(z^m)^n$ to $z^{mn}$. 

Simplifying expressions from $y^m\div y^n$ to $y^{m-n}$. 

Simplifying expressions from $x^mx^n$ to $x^{m+n}$. 

Simplifying expressions from $(8^m)^n$ to $8^{mn}$. 

Simplifying expressions from $3^m\div 3^n$ to $5^{m-n}$ where $n$ can be bigger then $m$.

Simplifying expressions from $5^m\div 5^n$ to $5^{m-n}$. 

Simplifying expressions from $2^m2^n$ to $2^{m+n}$. 

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Use this as a template to create Shear and Bending Moment diagram problems.   Supports concentrated forces and moments, uniformly distributed loads, and uniformly varying loads.

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Some basic tasks involving vectors, including converting to/from component form, scalar product, resultant vectors.

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$A,\;B$ $2 \times 2$ matrices. Find eigenvalues and eigenvectors of both. Hence or otherwise, find $B^n$ for largish $n$.

A variety of trigonometric equations which can be solved using inverse operations.

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Friction

Friction