Common Exponents
The terms exponents (or indexes) and 'powers' refer to the same thing.
We often encounter a power of $2$2 when measuring area. Consider, for example, the area of a square which is given by side length times side length. A number $x$x with an index of $2$2 is often read as $x$x to the power of $2$2 (or $x$x squared). You can express this as $x^2$x2.
$x$x to the power of $3$3 is also known as $x$x cubed which can be expressed as $x^3$x3. A power of $3$3 is involved in calculations like measuring the volume of a cube.
When we talk about exponents, it is important to remember the difference between the index and the base.
For example, in $10^3$103, $10$10 is the base number and $3$3 is the index number:
Hint: Think of the 'base' as that being closest to the ground, and the index is 'in' the air.
Examples
Question 1
State the base for the expression $3^2$32.
Question 2
Identify the power for the expression $4^6$46.
$6$6
A$4$4
B
Question 3
Write an expression for:
"$y$y raised to the power of $8$8."