Simplify (2x^3)^2 Step by Step

Step by step

Question: simplify (2x³)².

(2x³)²

The power 2 outside the bracket means: the whole bracket, 2 times.

(2x³)² = (2x³)(2x³)

So we write the bracket out, times itself.

= ((2x³))((2x³))

In times, the order does not matter.

So numbers go with numbers, and each letter goes with the same letter.

order does not matter: ab = ba

We put them in groups.

= (2 × 2)(x³ x³)

A power tells how many times the letter is multiplied.

x³ is 3 x's.

Together that is 6 x's.

x³ x³ = (xxx)(xxx) = x⁶

So the rule is: same letter, times, add the powers.

3 plus 3 is 6.

3 + 3 = 6

x^a x^b = x^{a + b}

3, added 2 times, is 3 times 2.

So for a power of a power, the rule is: multiply the powers.

3 × 2 = 6

(x^a)^b = x^{a × b}

2 times 2 is 4.

So we get 4x⁶.

= 4x⁶

Let's look back.

First: write the power out.

Then: numbers with numbers.

Last: count the letters.

Answer

= 4x⁶