An alternative word for exponent or index.  Used when reading exponents above 3.  E.g. 2^4 is read as “2 to the power of 4”.

Vinculum is the horizontal line placed over an expression to show that everything below that line is one group.

Problem solving with the laws of indices

Maths

Checking and securing understanding of converting between fractions and decimals

Checking and securing understanding of calculating with fractions and decimals

Checking and securing understanding of prime factorisation

Checking and securing understanding of LCM and HCF

Checking and securing understanding of roots and integer indices

Checking and securing understanding of calculations involving negative numbers

The laws of indices - multiplication

The laws of indices - division

The laws of indices - raising a power to a power

The laws of indices - negative and zero exponents

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 $$x$$ for $$(3^3)^4 \times 3^2 = 3^x$$ ?

What is the value of $$x$$ for $$\frac{2^{12} \times 2^4}{2^{10}} = 2^x $$?

What is the value of $$x$$ for $$\frac{5^{14} \times 5^5}{5^{-2}} = 5^x $$?

What is the value of $$x$$ for $$3^2 \times 3^6 = 9^x$$ ?

What is the value of $$x$$ for $$2^3 \times 4^3 = 2^x$$ ?

What is the value of $$x^{4x}$$ for $$2^x \times 2^{3x} = x^{4x}$$ ?

Evaluate $$16^\frac{1}{2}$$, giving the positive solution where necessary.

Evaluate $$9^\frac{3}{2}$$, giving the positive solution where necessary.

Evaluate $$25^\frac{1}{2}$$, giving the positive solution where necessary.

What is the value of $$b$$ for $$b^7 \div b^5 =9^2$$?

What is the value of $$k$$ for $$0.2^5 \div 0.2^k = 0.2^7$$?

What number is written as $$2^3 \times 5 \times 7$$ as a product of its prime factors? 

Starter Quiz

Evaluate $$16^\frac{1}{2}$$, giving the positive solution where necessary.