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).

A numerical coefficient is a constant multiplier of the variables in a term.

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”.

The laws of indices - raising a power to a power

Maths

In this unit, pupils formalised their understanding of the index laws. This understanding will allow them to perform calculations with values written in standard form more efficiently.

The conditions for standard form mean that pupils have explored how different powers of 10 can be written in the prior unit. In this unit, this understanding is generalised and the index laws formalised.

Arithmetic procedures: index laws

What is the value of $$x$$ for $$(m^3)^2 = m^x$$ ?

What is the value of $$x$$ for $$(p^8)^2 = p^x$$ ?

What is the value of $$x$$ for $$(m^x)^6 = m^{24}$$ ?

What is the positive value of $$x$$ for $$(m^x)^x = m^{16}$$ ?

What is the value of $$x$$ for $$(x^3)^3 = 5^9$$ ?

What is the value of $$x$$ for $$(x^x)^2 = x^6$$ ?

What is the value of $$b$$ for $$b^7 \div b^4 =9^3$$?

What is the value of $$c$$ for $$8^9 \times 8^4 = 8^c$$?

What is the value of $$b$$ for $$7^{-9} \div 7^4 = 7^b$$?

What is the value of $$k$$ for $$0.6^5 \div 0.6^k = 0.6^{-1}$$?

What is the value of $$k$$ for $$9^{(2k)} \div 9^k = 9^8$$?

What is the value of $$m$$ for $$m^9 \div m^7 = 6^2$$?

This lesson will be removed by end of Summer Term 2025.

The laws of indices - raising a power to a power

Lesson outcome

This lesson will be removed by end of Summer Term 2025.