Simplify (2x³)⁴.

Step by step, with the reason for every step · IGCSE Maths Extended Paper 2 · IGCSE Maths

Step by step

Question: simplify (2x³)⁴.

(2x³)⁴

The rule: a power outside a bracket goes on each part inside.

And for a power of a power, we multiply the powers.

(ab)ⁿ = aⁿbⁿ

(x^a)^b = x^{a × b}

So each part inside gets the power 4.

= 2⁴(x³)⁴

2⁴ is 2 times 2 times 2 times 2, which is 16.

2⁴ = 2 × 2 × 2 × 2

= 16

So 2⁴ becomes 16.

For x³ to the power 4, we multiply the powers.

= 16x^{3 × 4}

3 times 4 is 12.

So we get 16x¹².

= 16x¹²

Answer

= 16x¹²

Try this one yourself, then check your answer:

Simplify (2x²)³

Show the answer

8x⁶