Indices
India
Class IX
Simplify expressions using multiple index laws with integer and variable bases
Lesson
We've learnt lots of index laws now: the multiplication law, the division law, the power of a power law and the zero index law.
Now we are going to look at questions that we solve by using a combination of these rules. It's important to remember the order of operations when solving these questions as this is the order we apply.
Examples
Question 1
Simplify: $p^7\div p^3\times p^5$p7÷p3×p5.
Think: Following the order of operations, we'll use the division law and the multiplication law since they all have like bases.
Do:
| $p^7\div p^3\times p^5$p7÷p3×p5 | $=$= | $p^{7-3+5}$p7−3+5 |
| $=$= | $p^9$p9 |
Question 2
Simplify $\frac{\left(x^2\right)^6}{\left(x^2\right)^2}$(x2)6(x2)2
Question 3
Simplify $\left(u^9\times u^5\div u^{19}\right)^2$(u9×u5÷u19)2, expressing your answer in positive index form.