Multiplying indices

Example

Simplify c^3 \times c^2.

To answer this question, write c^3 and c^2 out in full: c^3 = c \times c \times c and c^2 = c \times c.

\mathbf{c^3} \times c^2 = \mathbf{c \times c \times c} \times c \times c. Writing the indices out in full shows that c^3 \times c^2 means c has now been multiplied by itself 5 times. This means c^3 \times c^2 can be simplified to c^5.

However, d^3 \times e^2 cannot be simplified because d and e are different.

curriculum-key-fact
To multiply together two identical values or variables (letters) that are presented in index form, add the powers. Example: b^5 \times b^3 = b^{5+3} = b^8.