Which expression is equivalent to (2x^3)^2? A) 2x^6 {forgot to… Step by Step

Step by step

The question

Question: simplify (2x³)².

(2x³)²

There are four choices.

First we solve it, the normal way.

Then we pick.

1 Write the power out

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))

2 Numbers with numbers

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)

3 Count the letters

A power tells how many times the letter is multiplied.

x³ is 3 x's multiplied.

Together that is 6 x's multiplied.

x³ x³ = (xxx)(xxx) = x⁶

So the rule: when we multiply the same letter, we 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

4 Pick the choice

Our answer is 4x⁶.

That is choice C.

C) 4x⁶

5 Why not the others

A is 2x⁶.

Wrong: forgot to square the 2: 2 × 2 = 4.

A) 2x⁶ ✗ forgot to square the 2: 2 × 2 = 4

B is 4x⁵.

Wrong: 3 + 2: a power of a power multiplies, 3 × 2.

B) 4x⁵ ✗ 3 + 2: a power of a power multiplies, 3 × 2

D is 2x⁵.

Wrong: forgot to square the 2 and added the powers.

D) 2x⁵ ✗ forgot to square the 2 and added the powers

Let's look back.

First: write the power out.

Then: numbers with numbers.

Then: count the letters.

Then: pick the choice.

Last: why not the others.

Answer