# PSAT Math : How to multiply exponents

## Example Questions

### Example Question #11 : Exponents

(x3)2 * x2

x2

x4

x6

x

x4

x4

Explanation:

When an exponent is raised to a power, we multiply. But when two exponents with the same base are multiplied, we add them. So (x3)2 = x3*2 = x6. Then (x3)2 * x2 = x6 * x2 = x6 – 2 = x4.

### Example Question #11 : Exponents

If , then which of the following is equivalent to ?

6^7

6^4

6^8 6^6 Explanation:

We can break up the equation into two smaller equations involving only x and y. Then, once we solve for x and y, we can find the value of . ### Example Question #41 : Exponents

If which of the following must be true?

I. II. III. I

III

None

All

II

None

Explanation: must be negative because it has an odd power and and have even powers above. But and could be positive or negative, so none of the scenarios has to be true.

### Example Question #11 : How To Multiply Exponents       Explanation:  Hence the correct answer will be ### Example Question #11 : Exponents

Solve for :       Explanation:

If Then  and Hence ### Example Question #51 : Exponents       Explanation:

(x3y6z)(x2yz3)

The paraentheses are irrelevant. Rearrange to combine like terms.

x3x2y6y1z1z3

When you multiply variables with exponents, simply add the exponents together.

x3+2 y6+1 z1+3

x5y7z4

### Example Question #51 : Exponents

If an original bacteria colony contains six organisms, and triples every hour, how many organisms are there after 7 hours?      Explanation:

To find the answer we can apply the equation of population where is the number of hours.

### Example Question #491 : Algebra

Simplify:       Explanation:

Use the distributive property: .  When we multiply variables with exponents, we keep the same base and add the exponents: ### Example Question #12 : Exponents

Simplify:       Explanation:  We cannot combine with , so .

### Example Question #492 : Algebra

If , then what is the value of ?       