Laws of indices - EdexcelMultiplying indices

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.