# Algebra 1b: Unit 1 Obj 3 ~ Simplify Division Of Like Bases

Approved & Edited by ProProfs Editorial Team
The editorial team at ProProfs Quizzes consists of a select group of subject experts, trivia writers, and quiz masters who have authored over 10,000 quizzes taken by more than 100 million users. This team includes our in-house seasoned quiz moderators and subject matter experts. Our editorial experts, spread across the world, are rigorously trained using our comprehensive guidelines to ensure that you receive the highest quality quizzes.
Learn about Our Editorial Process
| By Vicki Barr
V
Vicki Barr
Community Contributor
Quizzes Created: 14 | Total Attempts: 2,242
Questions: 11 | Attempts: 126

Settings

Rules of exponents: subtract exponents when like bases are divided

• 1.

### When a problem is asking to divide two base numbers that are the same, but with different exponents, what operation do I use for the exponents?

• A.

• B.

Subtract

• C.

Multiply

• D.

Divide

B. Subtract
Explanation
When dividing two base numbers with different exponents, you subtract the exponents. This is because when dividing, you are essentially canceling out the common factors between the two numbers. Subtracting the exponents ensures that you are dividing the base numbers correctly and obtaining the correct result.

Rate this question:

• 2.

### All bases have an exponent

• A.

True

• B.

False

A. True
Explanation
When a base has no exponent written it is assumed to be 1, thus all bases have an exponent even if none is written.

Rate this question:

• 3.

### Any base raised to this power will equal one

0
zero
Explanation
Any number raised to the power of zero equals one. This is a fundamental rule in mathematics. Therefore, any base raised to the power of zero will also equal one. In this case, the base is zero, so zero raised to the power of zero equals one.

Rate this question:

• 4.

### Simplify

• A.

4x^3/y

• B.

4x/y

• C.

X^3y/4

• D.

4y/x^3

A. 4x^3/y
Explanation
The given expression is 4x^3/y. To simplify this expression, we can divide both the numerator and denominator by 4. This gives us x^3/y. Therefore, the correct answer is x^3/y.

Rate this question:

• 5.

C.
• 6.

### 3a5b2/9a2b5

• A.

5ab^8

• B.

15a^2

• C.

A^3/3b^3

C. A^3/3b^3
Explanation
The given expression is a division of two terms. In the numerator, we have a^3, which means a multiplied by itself three times. In the denominator, we have 3b^3, which means 3 multiplied by b multiplied by itself three times. When we divide a^3 by 3b^3, we can simplify the expression by canceling out common factors. We can cancel one 'a' from the numerator with one 'a' from the denominator, leaving us with a^2 in the numerator. Similarly, we can cancel one 'b' from the numerator with one 'b' from the denominator, leaving us with 3b^2 in the denominator. Therefore, the simplified expression is a^2/3b^2.

Rate this question:

• 7.

### Write as a single power.

d^2
Explanation
The given expression, d^2, represents d raised to the power of 2. This means that d is multiplied by itself.

Rate this question:

• 8.

3125
• 9.

### Write as a single power.

m^9
Explanation
The given expression, m^9, represents m raised to the power of 9. This means that m is multiplied by itself 9 times.

Rate this question:

• 10.

### Simplify

• A.

15a^2

• B.

15a^3

• C.

15a^3b^0

• D.

28a^3b^0

• E.

28a^3

B. 15a^3
Explanation
The correct answer is 15a^3 because it is the simplest form of the given expressions. The other options have additional terms or factors that can be simplified or removed.

Rate this question:

• 11.
• A.

A

• B.

B

• C.

C

• D.

D

• E.

E