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Pre-Algebra : Pre-Algebra

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Example Questions

Example Question #4 : Product Rule Of Exponents

Simplify the following expression:

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

Possible Answers:

-9x^2y^9z^2

x^2y^1^8z^4

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

-20x^3y^9z^4

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 #5 : Product Rule Of Exponents

Simplify the following expression:

4y^4(-4xy^2)

Possible Answers:

-16xy^6

-16x^8y^8

-16 + xy^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 #1 : Product Rule Of Exponents

Simplify the following expression:

2x^2(-3x^3)

Possible Answers:

-6x - 23

-6x^5

-6x^6

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 #6 : Product Rule Of Exponents

Simplify:

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

Possible Answers:

$125 t^{3}$

$1 5 t^{6}$

$125 t^{9}$

$1 5 t^{9}$

$125 t^{6}$

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:

$\small 7x^5$

$\small 6x^6$

$\small 12x^5$

` $\small 12x^6$

$\small 6x^5$

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 #511 : Pre Algebra

Simplify:

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

Possible Answers:

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

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

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

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

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 #512 : Pre Algebra

Evaluate:

5x(y+3+2x)

Possible Answers:

25x +15xy

7x+y+3

5xy +7+7x

5xy +15x+10x^2

15xy+10x^2

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

$x^{-5}$

$x^{-6}$

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 #513 : Pre Algebra

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

Possible Answers:

6x^6

6x^5

3x^6

9x^5

3x^5

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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Example Question #514 : Pre Algebra

Simplify: x^3*y^4

Possible Answers:

x*y^7

(xy)^7

12xy

This expression is already simplified

$(xy)^{12}$

Correct answer:

This expression is already simplified

Explanation:

The product rule tells us that if we're multiplying 2 terms with exponents, we add the exponents. However, that is only applicable for 2 terms with the same base. In this case, our bases are different variables, so we can't use the product rule. This expression is as simplified as possible.

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Pre-Algebra : Pre-Algebra

Study concepts, example questions & explanations for Pre-Algebra

All Pre-Algebra Resources

Example Questions

Example Question #4 : Product Rule Of Exponents

Example Question #5 : Product Rule Of Exponents

Example Question #1 : Product Rule Of Exponents

Example Question #6 : Product Rule Of Exponents

Example Question #1 : Product Rule Of Exponents

Example Question #511 : Pre Algebra

Example Question #512 : Pre Algebra

Example Question #13 : Product Rule Of Exponents

Example Question #513 : Pre Algebra

Example Question #514 : Pre Algebra

All Pre-Algebra Resources

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