The laws of indices - multiplication | Maths | Quizalize & Oak National Academy

Starter quiz

Calculate $-3 \times 5^2$

'-75' ✓
Calculate $-3 \times 4^2$

'-48' ✓
Calculate $-3 \times 2^2$

'-12' ✓
Calculate $-4 \times 4^2$

'-64' ✓
Calculate $3^2 + (-4)^2$

'25' ✓
Calculate $9^2 + (-5)^2$

'106' ✓

Exit quiz

What is the value of $a$ for $3^3 \times 3^a = 3^{20}$ ?

'17' ✓
What is the value of $a$ for $3^3 \times 3^a = 3^7$ ?

'4' ✓
What is the value of $a$ for $5^8 \times 5^a = 5^{10}$ ?

'2' ✓
What is the value of $a$ for $3^3 \times a^7 = 3^{10}$ ?

'3' ✓
What is the value of $a$ for $3^7 \times a^8 = 3^{15}$ ?

'3' ✓
What is the value of $a$ for $6^3 \times 6^8 = 6^a$ ?

'11' ✓

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Lesson Details

Key learning points

When multiplying two terms, you can sometimes write this more simply.
If the powers have the same base, then the powers can be combined into a single power.
The exponent or index of the new power reflects this combination.
By studying the structure of multiplication, you can see how the index will change.
a^b × a^c = a^(b+c)

Common misconception

When multiplying terms with coefficients, pupils also add the coefficients as well as the exponents.

Pupils should be encouraged to rewrite their expression using the associative and commutative laws, with the number parts grouped and powers grouped. This hopefully avoids this error as they can see it is the product of the numbers.

Keywords

Power - 16 is the fourth power of 2. Alternatively this can be written as 2^4 which is read as “2 to the power of 4”.
Index - An exponent is a number positioned above and to the right of a base value. It indicates repeated multiplication. An alternative word for this is index (plural indices).
Coefficient - A numerical coefficient is a constant multiplier of the variables in a term.
Commutative - An operation is commutative if the values it is operating on can be written in either order without changing the calculation.
Associative - An operation is associative if a repeated application of the operation produces the same result regardless of how pairs of values are grouped.