Law Of Indices
In this lesson on the Law of Indices, students will learn how to simplify expressions involving powers using key rules. These include adding indices when multiplying, subtracting when dividing, and multiplying when raising a power. Mastering these laws helps simplify algebraic expressions and builds a strong foundation for more advanced maths topics.
Related Lessons:
Law Of Indices
In this video, we will explore the different laws of indices. To make the law easier to remember, the laws are grouped into logical categories, such as combining powers with the same base and combining bases with the same power.
Law Of Indices Example 1
Simplify, leaving your answer in positive index notation
- \(35x^2Γ·5x^{-4}\)
- \((4π₯^6 )^{\frac{1}{2}}\)
Law Of Indices Example 2
Simplify \(\frac{π¦^6Γβπ¦}{π¦^3}\) , giving your answer in the form \(π¦^π\) where n is a rational number.
Law Of Indices Example 3
Simplify \(\frac{2π^3Γ3π^{β2}}{βπ}\), leaving your answer in positive index notation.
Law Of Indices Example 4
Simplify \((π^{β\frac{ 3}{4}} π^{\frac{1}{3}} )^2ΓβπΓ·β(π^{β5} )\), leaving your answer in positive index notation.
Law Of Indices Example 5
- \(βπ§^{β6}\)
- \((pq^2)^{-5}Γ\frac{q^0}{p^3}Γ·(p^{-3}q)^3\)
Law Of Indices Example 6
Simplify, \(\frac{(3ππ^2 )^2}{β(8π^6 )}Γ·15π^2 π\) leaving your answer in positive index notation.
Law Of Indices Example 7
Given that \(\frac{π‘^6Γβπ‘^2}{π‘^{β1}} =π‘^π\), find the value of n.
Law Of Indices Example 8
Β Given that \(\frac{π₯^{\frac{3}{2}}Γπ₯^{β3}}{βπ₯}=π₯^π\), find the value of n.
Law Of Indices Example 9
Solve the equation \(4^π₯=\frac{1}{32}\)
Law Of Indices Example 10
Solve the equation \(16=8^{\frac{1}{π₯}}\)