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

Step by step

Question: simplify (x³y)².

(x³y)²

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

(x³y)² = (x³y)(x³y)

So we write the bracket out, times itself.

= ((x³y))((x³y))

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

y y = (y)(y) = y²

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

3 plus 3 is 6.

For y: 1 plus 1 is 2.

3 + 3 = 6

y: 1 + 1 = 2

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 x⁶y².

= x⁶y²

Let's look back.

First: write the power out.

Last: count the letters.

Answer

= x⁶y²