Which expression is equivalent to (x^3)(x^4)? A) x^7 B) x^12 {3 × 4…

Step by step, with the reason for every step · SAT: Equivalent expressions · SAT Math

Step by step

Question: simplify ((x³))((x⁴)).

Brackets next to each other mean times.

((x³))((x⁴))

There are four choices.

First we solve it, the normal way.

Then we pick.

A power tells how many times the letter is multiplied.

x³ is 3 x's multiplied.

x⁴ is 4 x's multiplied.

Together that is 7 x's multiplied.

x³ x⁴ = (xxx)(xxxx) = x⁷

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

3 plus 4 is 7.

3 + 4 = 7

x^a x^b = x^{a + b}

So we get x⁷.

= x⁷

Our answer is x⁷.

That is choice A.

A) x⁷

B is x¹².

Wrong: 3 × 4: multiplied the powers; we add them.

B) x¹² ✗ 3 × 4: multiplied the powers; we add them

C is 2x⁷.

Wrong: x × x is x², not 2x.

C) 2x⁷ ✗ x × x is x², not 2x

D is 2x¹².

Wrong: multiplied the powers and doubled.

D) 2x¹² ✗ multiplied the powers and doubled

Let's look back.

First: count the letters.

Then: pick the choice.

Last: why not the others.

Answer

= x⁷

Try this one yourself, then check:

Simplify ((x³))((x⁵))

Show the answer

x⁸