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

Advanced problem solving with the laws of indices

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 $$(3^3)^4 × 3^2 = 3^x$$ ?

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