Indices are used to show numbers that have been multiplied by themselves. They can be used instead of the roots such as the square root. The rules make complex calculations that involve powers easier.
simplifyA fraction is simplified when there are no more common factors shared by the numerator and denominator. For example, the fraction 8/10 simplifies to 4/5 by dividing the numerator and denominator by the common factor of 2.\(c^3 \times c^2\).
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.