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

1) Any base raised to this power will equal one

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.

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.

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2) Write as a single power.

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

Explanation

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

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4) Write as a single power.

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

Explanation

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

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5) 3a⁵b²/9a²b⁵

5ab^8

15a^2

A^3/3b^3

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.

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.

6) 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?

Add

Subtract

Multiply

Divide

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.

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.

7) Simplify

4x^3/y

4x/y

X^3y/4

4y/x^3

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.

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.

8) Which one do you like?

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Explanation

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9)

fraction numerator 8 u to the power of 4 v to the power of 10 over denominator minus 2 u squared v to the power of 8 end fraction a n s w e r s : A. space space minus 4 u squared v squared B. space space minus 7 u v cubed C. space space minus 4 u to the power of 7 v squared D. space space 6 u squared v squared E. space space minus 4 u to the power of 6 v to the power of 18

A

B

C

D

E

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Explanation

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10) ^{Simplify $fraction numerator 30 a to the power of 9 b squared over denominator 2 a to the power of 6 b squared end fraction$}

15a^2

15a^3

15a^3b^0

28a^3b^0

28a^3

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.

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.

11) All bases have an exponent

True

False

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

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.