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.

\(b^5 × b^3 = b^8\)

Simplify \(6a^3b^5 × 4ab^3\)

\(6 \times 4 = 24.\)

Remember that \(a = a^1\). So \(a^3 × a = a^3 × a^1 = a^{3+1} = a^4.\)

\(b^5 × b^3 = b^{5+3} = b^8\).

\(6a^3b^5 × 4ab^3 = 24a^4b^8\).