# Exponents, roots and logarithms

Here is a list of all of the skills that cover exponents, roots and logarithms! These skills are organised by year, and you can move your mouse over any skill name to preview the skill. To start practising, just click on any link. IXL will track your score, and the questions will automatically increase in difficulty as you improve!

## Year 8 skills

- A.8 Standard form
- A.9 Compare numbers written in standard form
- I.1 Understanding exponents
- I.2 Evaluate exponents
- I.3 Solve equations with variable exponents
- I.4 Exponents with negative bases
- I.5 Exponents with decimal and fractional bases
- I.6 Evaluate numerical expressions involving exponents
- I.7 Square roots of perfect squares
- I.8 Estimate square roots
- M.11 Compound interest

## Year 9 skills

- F.1 Understanding exponents
- F.2 Evaluate exponents
- F.3 Solve equations with variable exponents
- F.4 Exponents with negative bases
- F.5 Exponents with decimal and fractional bases
- F.6 Understanding negative exponents
- F.7 Evaluate negative exponents
- F.8 Multiplication with exponents
- F.9 Division with exponents
- F.10 Multiplication and division with exponents
- F.11 Power rule
- F.12 Evaluate expressions using properties of exponents
- F.13 Identify equivalent expressions involving exponents
- F.14 Square roots of perfect squares
- F.15 Positive and negative square roots
- F.16 Estimate square roots
- F.17 Relationship between squares and square roots
- F.19 Cube roots of perfect cubes
- F.20 Estimate cube roots
- F.21 Solve equations involving cubes and cube roots
- G.1 Convert between ordinary numbers and standard form
- G.2 Compare numbers written in standard form
- G.3 Multiply numbers written in standard form
- G.4 Divide numbers written in standard form
- K.9 Compound interest
- V.7 Evaluate radical expressions
- AA.9 Powers of monomials
- AA.10 Square and cube roots of monomials

## Year 10 skills

- A.5 Square roots
- A.6 Cube roots
- D.7 Compound interest
- R.1 Exponents with integer bases
- R.2 Exponents with decimal and fractional bases
- R.3 Negative exponents
- R.4 Multiplication with exponents
- R.5 Division with exponents
- R.6 Multiplication and division with exponents
- R.7 Power rule
- R.8 Evaluate expressions using properties of exponents
- R.9 Identify equivalent expressions involving exponents
- S.1 Convert between ordinary numbers and standard form
- S.2 Compare numbers written in standard form
- S.3 Multiply numbers written in standard form
- S.4 Divide numbers written in standard form
- T.5 Powers of monomials
- W.1 Simplify radical expressions
- W.2 Simplify radical expressions with variables
- W.3 Simplify radical expressions involving fractions
- W.4 Multiply radical expressions
- W.5 Add and subtract radical expressions
- W.6 Simplify radical expressions using the distributive property
- W.7 Divide radical expressions
- W.8 Simplify radical expressions: mixed review
- X.1 Evaluate rational exponents
- X.2 Multiplication with rational exponents
- X.3 Division with rational exponents
- X.4 Power rule with rational exponents
- X.5 Simplify expressions involving rational exponents I
- X.6 Simplify expressions involving rational exponents II

## Year 11 skills

- A.3 Square roots
- A.4 Cube roots
- C.2 Compound interest
- C.3 Continuously compounded interest
- K.1 Exponents with integer bases
- K.2 Exponents with decimal and fractional bases
- K.3 Negative exponents
- K.4 Multiplication with exponents
- K.5 Division with exponents
- K.6 Multiplication and division with exponents
- K.7 Power rule
- K.8 Evaluate expressions using properties of exponents
- K.9 Identify equivalent expressions involving exponents
- L.1 Convert between exponential and logarithmic form: rational bases
- L.2 Evaluate logarithms
- L.3 Change of base formula
- L.4 Identify properties of logarithms
- L.5 Product property of logarithms
- L.6 Quotient property of logarithms
- L.7 Power property of logarithms
- L.8 Properties of logarithms: mixed review
- L.9 Evaluate logarithms: mixed review
- M.1 Domain and range of exponential and logarithmic functions
- M.2 Evaluate an exponential function
- M.3 Match exponential functions and graphs
- M.4 Solve exponential equations by factorising
- M.5 Solve exponential equations using common logarithms
- M.6 Solve logarithmic equations I
- M.7 Solve logarithmic equations II
- M.8 Exponential growth and decay: word problems
- N.5 Powers of monomials
- R.5 Exponential functions over unit intervals
- R.6 Describe linear and exponential growth and decay
- U.1 Simplify radical expressions
- U.2 Simplify radical expressions involving fractions
- U.3 Multiply radical expressions
- U.4 Add and subtract radical expressions
- U.5 Simplify radical expressions using the distributive property
- U.6 Simplify radical expressions: mixed review
- V.1 Evaluate rational exponents
- V.2 Multiplication with rational exponents
- V.3 Division with rational exponents
- V.4 Power rule with rational exponents
- V.5 Simplify expressions involving rational exponents I
- V.6 Simplify expressions involving rational exponents II

## Year 12 skills

- K.1 Roots of integers
- K.2 Roots of rational numbers
- K.3 Find roots using a calculator
- K.4 Nth roots
- K.5 Simplify radical expressions with variables I
- K.6 Simplify radical expressions with variables II
- K.7 Multiply radical expressions
- K.8 Divide radical expressions
- K.9 Add and subtract radical expressions
- K.10 Simplify radical expressions using the distributive property
- K.11 Simplify radical expressions using conjugates
- K.12 Domain and range of radical functions
- K.13 Solve radical equations
- L.1 Evaluate rational exponents
- L.2 Multiplication with rational exponents
- L.3 Division with rational exponents
- L.4 Power rule
- L.5 Simplify expressions involving rational exponents I
- L.6 Simplify expressions involving rational exponents II
- P.1 Convert between exponential and logarithmic form: rational bases
- P.2 Convert between natural exponential and logarithmic form
- P.3 Convert between exponential and logarithmic form: all bases
- P.4 Evaluate logarithms
- P.5 Evaluate natural logarithms
- P.6 Change of base formula
- P.7 Identify properties of logarithms
- P.8 Product property of logarithms
- P.9 Quotient property of logarithms
- P.10 Power property of logarithms
- P.11 Properties of logarithms: mixed review
- P.12 Evaluate logarithms: mixed review
- Q.1 Domain and range of exponential and logarithmic functions
- Q.2 Evaluate exponential functions
- Q.3 Match exponential functions and graphs
- Q.4 Solve exponential equations by factorising
- Q.5 Solve exponential equations using common logarithms
- Q.6 Solve exponential equations using natural logarithms
- Q.7 Solve logarithmic equations I
- Q.8 Solve logarithmic equations II
- Q.9 Identify linear and exponential functions
- Q.10 Exponential functions over unit intervals
- Q.11 Describe linear and exponential growth and decay
- Q.12 Exponential growth and decay: word problems
- Q.13 Compound interest: word problems
- Q.14 Continuously compounded interest: word problems

## Year 13 skills

- E.1 Domain and range of exponential and logarithmic functions
- E.2 Convert between exponential and logarithmic form
- E.3 Evaluate logarithms
- E.4 Change of base formula
- E.5 Product property of logarithms
- E.6 Quotient property of logarithms
- E.7 Power property of logarithms
- E.8 Evaluate logarithms using properties
- E.9 Solve exponential equations by factorising
- E.10 Solve exponential equations using logarithms
- E.11 Solve logarithmic equations with one logarithm
- E.12 Solve logarithmic equations with multiple logarithms
- E.13 Identify linear and exponential functions
- E.14 Exponential functions over unit intervals
- E.15 Describe linear and exponential growth and decay
- E.16 Exponential growth and decay: word problems
- E.17 Compound interest: word problems