Which expression is equivalent to (x^2)(x^6)?

Step by step

The question

Question: which expression is equivalent to (x²)(x⁶)?

Equivalent means: the same value for every x.

Brackets next to each other mean times.

There are four choices.

First we simplify it, the normal way.

Then we pick.

1 Add the powers

The rule: when we multiply the same letter, we add the powers.

We add the powers of x.

2 plus 6 is 8.

So we get x⁸.

2 Pick the choice

Our answer is x⁸.

That is choice A.

3 Why not the others

B is 2x⁸.

Wrong: x × x is x², not 2x.

C is x¹².

Wrong: 2 × 6: multiplied the powers; we add them.

D is 2x¹².

Wrong: multiplied the powers and doubled.

Let's look back.

First: add the powers.

Then: pick the choice.

Last: why not the others.