We are exploring exponents and algebraic expressions.  We are looking at what an exponent means, and how coefficients change expressions, and how important brackets are.  We are representing coefficients here.  The corfficient shows how many of someing there are.The next set show what thee exponent 2 means.  It makes the model a square.  The coefficient, not in brackets, indicates how many squares we need.

Here is another example.

When the coefficient is a fraction, we need a fraction of the square.
An expression with a coefficient in brackets, and an exponent outside changes things.  The base of the exponent 2 in this case is 2x.  This means the side length of the square is 2x.  You will notice that this is equivalent to 4 x squared.

A similar relationship extends to the following…

An exponent of 3 makes the model a cube.

A coefficient outside brackets shows how many cubes to make.

And if the coefficient is in the brackets it shows the side length of the cube.  Here 8 x cubes could fit inside this bigger cube.

We are attempting to build (3x)^3 here, it’s a big challenge!  We need to make 27 cubes all linked up to make a big cube

Here is a tiny cube, one eigth of the x cube.  Note how (0.5)^3 is equal to 1/8.

We need to remember to pay close attention to the power, the coefficient, and whether there are brackets!