A reciprocal is the multiplicative inverse of any non-zero number. Any non-zero number multiplied by its reciprocal is equal to 1.

The laws of indices - fractional exponents

Maths

Converting any recurring decimal to a fraction

Checking and securing understanding of prime factorisation

Checking and securing understanding of LCM and HCF

Checking and securing understanding of roots and integer indices

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

Advanced problem solving with the laws of indices

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

Evaluate $$36^{\frac{1}{2}}$$, giving the positive solution where necessary.

Evaluate $$1000^{\frac{1}{3}}$$, giving the positive solution where necessary.

Evaluate $$27^{\frac{2}{3}}$$, giving the positive solution where necessary.

Evaluate $$1000^{\frac{2}{3}}$$, giving the positive solution where necessary.

Evaluate $$16^{\frac{3}{4}}$$, giving the positive solution where necessary.

Evaluate $$16^{\frac{3}{2}}$$, giving the positive solution where necessary.

What is the value of $$x$$ for $$(m^x)^8 = m^{32}$$

What is the value of $$x$$ for $$(m^{-2})^5 = m^x$$

What is the value of $$x$$ for $$(m^8)^x = m^{80}$$

What is the value of $$x$$ for $$\frac{1}{16} = 2^x$$

What is the value of $$x$$ for $$\frac{1}{64} = x^{-6}$$

What is the value of $$a$$ for $$7^9 \times 7^a = 7^6$$?

The laws of indices - fractional exponents

Lesson outcome