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

Starter quiz

What is the value of $a$ for $a^3 \times a^7 = 12^{10}$ ?

'12' ✓
What is the value of $a$ for $a^a \times a^a = 9^{18}$ ?

'9' ✓
What is the value of $a$ for $5^a \times 5^a = 5^{20}$ ?

'10' ✓
What is the value of $a$ for $8^6 \times 8^{-a} = 8^a$ ?

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

'0' ✓
What is the value of $a$ for $9^a = 81$ ?

'1' ✓

Exit quiz

What is the value of $b$ for $b^9 \div b^4 = 6^5$ ?

'6' ✓
What is the value of $a$ for $9^{20} \div 9^7 = 9^a$ ?

'13' ✓
What is the value of $a$ for $0.4^8 \div 0.4^a = 0.4$ ?

'7' ✓
What is the value of $a$ for $\frac{7^a}{7^7} = 7^{12}$ ?

'19' ✓
What is the value of $a$ for $\frac{5^9}{5^3} = 5^a$ ?

'6' ✓
What is the value of $a$ for $\frac{x^a}{x^8} = x^{10}$ ?

'18' ✓

Worksheet

Loading worksheet ...

Presentation

Loading presentation ...

Video

Lesson Details

Key learning points

When dividing 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 division, you can see how the index will change.
a^b ÷ a^c = a^(b−c)

Common misconception

When dividing terms with coefficients, pupils also subtract the coefficients as well as the exponents.

Pupils should be encouraged to rewrite their expression as a fraction, with the number parts grouped and powers grouped. This hopefully avoids this error as they can see the fraction line as a division.

Keywords

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.
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”.