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Pre-Algebra : Product Rule of Exponents

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Example Questions

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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Example Question #13 : Product Rule Of Exponents

Simplify: x^3*y^4

Possible Answers:

(xy)^7

This expression is already simplified

$(xy)^{12}$

12xy

x*y^7

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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Example Question #16 : Product Rule Of Exponents

Use the product rule of exponents to simplify: 5x^6(2x^4)+2y^3(x^2+3x^2)

Possible Answers:

2x^2(5x^8+4y^3)

$10x^{10}+2y^3(3x^2)$

$7x^{2}+2y^3(4x^2)$

None of the other answers.

8x^2(2x^8+y^3)

Correct answer:

2x^2(5x^8+4y^3)

Explanation:

The product rule states that when two like bases with the same power are being multiplied, we add the powers together and preserve the base. In mathematical language, $a^m*a^n=a^{m+n}$ . If constants are present in front of either base we multiply them as usual.

5x^6(2x^4)+2y^3(x^2+3x^2)

Combine using the power rule:

$10x^{10}+2y^3(x^2+3x^2)$

Combine the parenthesis:

$10x^{10}+2y^3(4x^2)$

$10x^{10}+8y^3x^2$

Factor fully:

2x^2(5x^8+4y^3)

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Example Question #17 : Product Rule Of Exponents

Simplify the following expression:

$z^{4} \times z^{3} \times z^{-2} \times y^{3}$

Possible Answers:

$z^{7}y$

$z^{5}y^{-3}$

$z^{-24}y^{3}$

$z^{5}y^{3}$

$z^{-5}y^{3}$

Correct answer:

$z^{5}y^{3}$

Explanation:

The product rule of exponents states that we can multiply two exponents with the same base by adding the exponents. The exponents of different bases cannot be summed, therefore our term will not change.

$z^{4} \times z^{3} \times z^{-2} \times y^{3}$

$4 + 3 + \left ( -2\right ) = 5$

Therefore, the simplest form of the expression is

$z^{5} \times y^{3}$ which can be written as $z^{5}y^{3}$

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Example Question #14 : Product Rule Of Exponents

Simplify:

(x^2)(x^4)

Possible Answers:

x^2

x^6

$x^{-2}$

x^8

Correct answer:

x^6

Explanation:

When you multiply exponents with the same base, you add the exponents:

(x^2)(x^4)=x^6

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Example Question #15 : Product Rule Of Exponents

Simplify:

(y^5)(y^9)

Possible Answers:

$y^{45}$

y^4

$y^{-4}$

$y^{14}$

Correct answer:

$y^{14}$

Explanation:

When you multiply exponents with the same base, you add the exponents:

$(y^5)(y^9)=y^{14}$

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Example Question #16 : Product Rule Of Exponents

Simplify:

$(z^6)(z^{-2})$

Possible Answers:

z^4

$z^{-4}$

z^8

$z^{-12}$

Correct answer:

z^4

Explanation:

When you multiply exponents with the same base, you add the exponents:

$(z^6)(z^{-2})=z^{4}$

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Pre-Algebra : Product Rule of Exponents

Study concepts, example questions & explanations for Pre-Algebra

All Pre-Algebra Resources

Example Questions

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

Example Question #13 : Product Rule Of Exponents

Example Question #16 : Product Rule Of Exponents

Example Question #17 : Product Rule Of Exponents

Example Question #14 : Product Rule Of Exponents

Example Question #15 : Product Rule Of Exponents

Example Question #16 : Product Rule Of Exponents

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