Simplify (x^2)^3 Step by Step

Step by step

Question: simplify (x²)³.

(x²)³

The power 3 outside the bracket means: the whole bracket, 3 times.

(x²)³ = (x²)(x²)(x²)

So we write the bracket out, times itself.

= ((x²))((x²))((x²))

A power tells how many times the letter is multiplied.

x² is 2 x's.

Together that is 6 x's.

x² x² x² = (xx)(xx)(xx) = x⁶

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

2 plus 2 plus 2 is 6.

2 + 2 + 2 = 6

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

2, added 3 times, is 2 times 3.

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

2 × 3 = 6

(x^a)^b = x^{a × b}

So we get x⁶.

= x⁶

Let's look back.

First: write the power out.

Last: count the letters.

Answer

= x⁶