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”.

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.

An operation is commutative if the values it is operating on can be written in either order without changing the calculation.

An operation is associative if a repeated application of the operation produces the same result regardless of how pairs of values are grouped.

The laws of indices - multiplication

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.

In this unit pupils learn how to manipulate indices and perform calculations without conversion by understanding index laws.

Arithmetic procedures: index laws

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

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

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

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

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

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

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