Which expression is equivalent to (3x^2)^3?

Step by step

The question

Question: which expression is equivalent to (3x²)³?

Equivalent means: the same value for every x.

There are four choices.

First we simplify it, the normal way.

Then we pick.

1 Power of a product

The rule: a power outside a bracket goes on each part inside.

And for a power of a power, we multiply the powers.

So each part inside gets the power 3.

3³ is 3 times 3 times 3, which is 27.

So 3³ becomes 27.

For x² to the power 3, we multiply the powers.

2 times 3 is 6.

So we get 27x⁶.

2 Pick the choice

Our answer is 27x⁶.

That is choice D.

3 Why not the others

A is 9x⁵.

Wrong: 3 × 3 and 2 + 3: a power of a power multiplies, and 3³ = 27.

B is 9x⁶.

Wrong: 3 × 3: but 3³ is 3 × 3 × 3 = 27.

C is 27x⁵.

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

Let's look back.

First: power of a product.

Then: pick the choice.

Last: why not the others.