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Pre-Algebra : Polynomials

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Example Questions

Example Question #3 : Product Rule Of Exponents

Simplify the following expression:

(7x^2)(3xy^5)

Possible Answers:

21x^3y^5

10x^3y^5

x^3 + y^5 + 10

21x^2y^5

Correct answer:

21x^3y^5

Explanation:

In the last few problems, we saw one way to multiply terms with exponents.

Another way to explain what we did is to say: "When you MULTIPLY terms together, simplify by ADDING the exponents of each variable."

Here's what that looks like in this case:

First multiply the coefficients: 7(3) = 21

Then ADD the exponents of the variables to simplify. In the first term, the exponent on the is 2. In the second term the exponent is 1. So we ADD 2 + 1 = 3 and have x^3 .

Only the second term has the variable and its exponent is 5. There is nothing to add onto that (because there are no 's in the first term), so it stays y^5 .

Remember, this is all being multiplied together, so the final answer is 21x^3y^5

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Example Question #1 : Product Rule Of Exponents

Simplify the following expression:

(5x^2y^3z^2)(-4xy^6z^2)

Possible Answers:

-20x^2y^1^8z^4

x^2y^1^8z^4

-20x^3y^9z^4

-9x^2y^9z^2

Correct answer:

-20x^3y^9z^4

Explanation:

(5x^2y^3z^2)(-4xy^6z^2)

Remember the rule:

"When you MULTIPLY terms together, simplify by ADDING the exponents of each variable."

Here's what that looks like in this case:

First multiply the coefficients: 5(-4)=-20

Then ADD the exponents of the variables to simplify. In the first term, the exponent on the is 2. In the second term the exponent is 1. So we ADD 2+1=3 and just have x^3 .

In the first term, the exponent on the is 3. In the second term the exponent is 6. So we ADD 3+6=9 and just have y^9 .

In the first term, the exponent on the is 2. In the second term the exponent is 2. So we ADD 2+2=4 and just have z^4 .

Remember, all these parts are being multiplied together, so the final answer is -20x^3y^9z^4

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Example Question #3 : Product Rule Of Exponents

Simplify the following expression:

4y^4(-4xy^2)

Possible Answers:

-16xy^6

-16 + xy^8

-16x^8y^8

Correct answer:

-16xy^6

Explanation:

The exponent represents how many times the term is being multiplied. So, for example, x^2 means (x)(x) and x^5 would be (x)(x)(x)(x)(x)

So the first term 4y^4 = 4(y)(y)(y)(y)

And the second term -4xy^2= -4(x)(y)(y)

Since the two terms are only separated by parentheses, they are being all multiplied together.

First multiply the coefficients, 4(-4) = -16

We also have a total of 6 's and 1 all being multipled together.

The final answer is -16xy^6

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Example Question #7 : Product Rule Of Exponents

Simplify the following expression:

2x^2(-3x^3)

Possible Answers:

-6x - 23

-6x^6

-6x^5

Correct answer:

-6x^5

Explanation:

The exponent represents how many times the term is being multiplied. So, for example, x^2 means (x)(x) and x^5 would be (x)(x)(x)(x)(x)

So the first term 2x^2 = 2(x)(x)

And the second term -3x^3 = -3(x)(x)(x)

Since the two terms are only separated by parentheses, they are being all multiplied together.

First multiply the coefficients, 2(-3) = -6

We also have a total of 's all being multipled together.

The final answer is -6x^5

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Example Question #4 : Product Rule Of Exponents

Simplify:

$\left (5t^{3} \right )^{ 3}$

Possible Answers:

$125 t^{3}$

$1 5 t^{9}$

$125 t^{9}$

$125 t^{6}$

$1 5 t^{6}$

Correct answer:

$125 t^{9}$

Explanation:

$\left (5t^{3} \right )^{ 3} = 5^{ 3} \cdot \left (t^{3} \right ) ^{ 3} = 125 t^{3 \cdot 3} = 125 t^{9}$

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Example Question #1 : Product Rule Of Exponents

Which of the following is equal to $3x^2\times 4x^3$ ?

Possible Answers:

$\small 6x^6$

` $\small 12x^6$

$\small 12x^5$

$\small 6x^5$

$\small 7x^5$

Correct answer:

$\small 12x^5$

Explanation:

Remember that when multiplying variables with exponents, the following property holds true:

$x^a\times x^b = x^{a+b}$

With this knowledge, we can solve the problem:

$3x^2\times 4x^3$

$=(3\times 4)x^2^+^3$

$\small =12x^5$

The answer is $\small 12x^5$ .

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Example Question #11 : Product Rule Of Exponents

Simplify:

$x^{3}y^{2}\cdot xy^{4}$

Possible Answers:

$x^{4}y^{8}$

$x^{4}y^{6}$

$x^{3}y^{6}$

$x^{3}y^{8}$

Correct answer:

$x^{4}y^{6}$

Explanation:

Use the product rule of exponents, which states that when multiplying expression(s) with the same base, you add the exponents together:

$x^{3+1}y^{4+2}$

Therefore the correct answer is $x^{4}y^{6}$ .

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Example Question #12 : Product Rule Of Exponents

Evaluate:

5x(y+3+2x)

Possible Answers:

7x+y+3

5xy +15x+10x^2

15xy+10x^2

25x +15xy

5xy +7+7x

Correct answer:

5xy +15x+10x^2

Explanation:

Distribute the to each of the terms and add them.

5xy +15x +10x^2

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Example Question #13 : Product Rule Of Exponents

Simplify: $x^3*x^{-2}$

Possible Answers:

x^5

$x^{-6}$

$x^{-5}$

Correct answer:

Explanation:

The general rule for multiplying terms with exponents is that we add the exponents together. In this case the exponents are and , and -2+3=1 . x^1 is just : anything to the first power is itself.

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Example Question #14 : Product Rule Of Exponents

Simplify: x^3*(3x)^2

Possible Answers:

9x^5

6x^6

6x^5

3x^5

3x^6

Correct answer:

9x^5

Explanation:

To simplify x^3*(3x)^2 it helps to understand what it means. x^3 just means x times itself 3 times, x*x*x . (3x)^2 means multiply times itself, or (3x)*(3x) . We can simplify that by multiplying 3*3 = 9 and x*x=x^2 . Multiplying both terms together gives us x*x*x*9*x*x . This is a 9 and 5 x's being multiplied together, or 9x^5 .

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Pre-Algebra : Polynomials

Study concepts, example questions & explanations for Pre-Algebra

All Pre-Algebra Resources

Example Questions

Example Question #3 : Product Rule Of Exponents

Example Question #1 : Product Rule Of Exponents

Example Question #3 : Product Rule Of Exponents

Example Question #7 : Product Rule Of Exponents

Example Question #4 : Product Rule Of Exponents

Example Question #1 : Product Rule Of Exponents

Example Question #11 : Product Rule Of Exponents

Example Question #12 : Product Rule Of Exponents

Example Question #13 : Product Rule Of Exponents

Example Question #14 : Product Rule Of Exponents

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