Simplify (y^3)^2 Step by Step

Step by step

Question: simplify (y³)².

(y³)²

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

(y³)² = (y³)(y³)

So we write the bracket out, times itself.

= ((y³))((y³))

A power tells how many times the letter is multiplied.

y³ is 3 y's.

Together that is 6 y's.

y³ y³ = (yyy)(yyy) = y⁶

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}

So we get y⁶.

= y⁶

Let's look back.

First: write the power out.

Last: count the letters.

Answer

= y⁶