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.\(b^5 \div b^3\).
\(b^5 \div b^3\) can be written as \(\frac{b^5}{b^3}\) and writing out the denominatorThe bottom part of a fraction. For â , the denominator is 8, which represents 'eighths'. and numeratorThe top part of a fraction. For â , the numerator is 5. in full gives \(\frac{b \times b \times b \times b \times b}{b \times b \times b}\). There are common factors of \(b\) in the numerator and denominator and these can be cancelled out, giving \(\frac{\cancel{b} \times \cancel{b} \times \cancel{b} \times b \times b}{\cancel{b} \times \cancel{b} \times \cancel{b}}\) which leaves \(b \times b = b^2\).
This means \(b^5 \div b^3\) can be simplified to \(b^2\).