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Powers and Roots
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Foundational skills
Understand squared notation
\[ 7^2 \]
Write 7² as a multiplication
Understand cubed notation
\[ 4^3 \]
Write 4³ as a multiplication
Understand general index notation
\[ 2^5 \]
Write 2⁵ as a multiplication
Identify the base and exponent
\[ 3^4 \]
In the expression 3⁴, what is the base and what is the exponent?
Recognise square numbers
\[ \text{Is 36 a square?} \]
Is 36 a square number?
Recognise cube numbers
\[ \text{Is 64 a cube?} \]
Is 64 a cube number?
Square numbers
Recall squares of 1 to 10
\[ 7^2 \]
What is 7²?
Recall squares of 11 to 15
\[ 13^2 \]
What is 13²?
Squares of multiples of 10
\[ 40^2 \]
What is 40²?
Squares of multiples of 100
\[ 300^2 \]
What is 300²?
Squares ending in 5
\[ 25^2 \]
What is 25²?
Square roots
Square roots up to √100
\[ \sqrt{49} \]
What is √49?
Square roots 121 to 225
\[ \sqrt{169} \]
What is √169?
Larger square roots
\[ \sqrt{400} \]
What is √400?
Square roots in context
\[ \text{Area } = 81 \]
A square has an area of 81 cm². What is the side length?
Cube numbers
Recall cubes of 1 to 5
\[ 4^3 \]
What is 4³?
Cubes of 6 to 9 and 10
\[ 10^3 \]
What is 10³?
Cube roots
Cube roots (small)
\[ \sqrt[3]{27} \]
What is ³√27?
Cube root of 1000
\[ \sqrt[3]{1000} \]
What is ³√1000?
Cube roots in context
\[ \text{Vol } = 64 \]
A cube has a volume of 64 cm³. What is the side length?
Higher powers
Calculate power 4
\[ 2^4 \]
What is 2⁴?
Calculate power 5
\[ 2^5 \]
What is 2⁵?
Higher powers of 2
\[ 2^8 \]
What is 2⁸?
Powers of 10
\[ 10^4 \]
What is 10⁴?
Recognising and expressing powers
Recognise powers of 2
\[ 2^? = 128 \]
Which power of 2 is equal to 128?
Recognise powers (small bases)
\[ 3^? = 81 \]
Which power of 3 is equal to 81?
Express as power of base
\[ 32 = 2^? \]
Write 32 as a power of 2
Express number as power
\[ 125 = ? \]
Write 125 as a power
Comparing and estimating
Compare powers
\[ 3^4 \text{ vs } 4^3 \]
Which is larger: 3⁴ or 4³?
Integers for square root
\[ \sqrt{50} \]
Between which two consecutive integers does √50 lie?
Estimate square roots
\[ \sqrt{40} \]
Estimate √40 to one decimal place
Integers for cube root
\[ \sqrt[3]{100} \]
Between which two consecutive integers does ³√100 lie?
Order integers and roots
\[ 7, \sqrt{60}, 8 \]
Put in order: 7, √60, 8, √45
Zero and power of one
Number to power of 1
\[ 15^1 \]
What is 15¹?
Number to power of 0
\[ 7^0 \]
What is 7⁰?
0 to positive power
\[ 0^5 \]
What is 0⁵?
Negative bases
Square negative number
\[ (-3)^2 \]
What is (-3)²?
Cube negative number
\[ (-2)^3 \]
What is (-2)³?
Negative to even power
\[ (-2)^4 \]
What is (-2)⁴?
Negative to odd power
\[ (-2)^5 \]
What is (-2)⁵?
Compare -n² and (-n)²
\[ -3^2 \text{ vs } (-3)^2 \]
Evaluate -5² and (-5)²
Timer (Optional)
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Question