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Pre-Algebra : Polynomials

Study concepts, example questions & explanations for Pre-Algebra

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Example Questions

Example Question #32 : Power Rule Of Exponents

Simplify the following:

(b^4)^9

Possible Answers:

b^9

$b^{36}$

$b^{49}$

b^5

$b^{13}$

Correct answer:

$b^{36}$

Explanation:

If you are raising a power to another power, you simply multiply the powers together. So,

$(b^4)^9 = b^{4 \cdot 9} = b^{36}$

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Example Question #33 : Power Rule Of Exponents

Simplify the following:

$(a^3)^4 + (b^2)^{-5}$

Possible Answers:

$a^7 + b^{-3}$

$a^{12} + b^{-10}$

$a^7b^{-3}$

$a^{12}b^{-10}$

(ab)^2

Correct answer:

$a^{12} + b^{-10}$

Explanation:

When raising a power to a power, we multiply the exponents. In this case, we get

$(a^3)^4 + (b^2)^{-5}$

$a^{3 \cdot 4} + b^{2 \cdot -5}$

$a^{12} + b^{-10}$

And since they have different bases, we cannot combine them any further.

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Example Question #34 : Power Rule Of Exponents

Which answer shows the answer to:

19^8 * 19^4 =

Possible Answers:

19^4

19^2

19^3^2

19^1^2

19^1^6

Correct answer:

19^1^2

Explanation:

19 is the base number. It is the same on both sides.

If the base is the same on both sides and it is a multiplication problem we keep the base and add the exponents together.

19^8 ^ + ^4

= 19^1^2

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Example Question #35 : Power Rule Of Exponents

Simplify the following:

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

Possible Answers:

$x^{-6}y^{-12}$

$x^{-1} + y^{-7}$

$x^{-6} + y^{-12}$

$x^{-5}y$

$x^{-5} + y$

Correct answer:

$x^{-6} + y^{-12}$

Explanation:

The power rule for exponents states that when you raise a power to a power, you multiply the exponents, keeping the base the same. So,

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

can be written as

$x^{\ 2 \ \cdot \ -3} + y^{\ -3 \ \cdot \ 4}$

$x^{-6} + y^{-12}$

Since we cannot combine two different bases, this is now in simplest form.

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Example Question #36 : Power Rule Of Exponents

Simplify the polynomial.

$(2m^{2}n^{4}y^{3})^{2}$

Possible Answers:

$4m^{4}n^{8}y^{6}$

$4mny^{18}$

$4m^{2}n^{4}y^{3}$

$4m^{4}n^{6}y^{5}$

$4mny^{8}$

Correct answer:

$4m^{4}n^{8}y^{6}$

Explanation:

In order to solve this problem you must take every integer and variable to the power of 2 like so,

$(2m^{2}n^{4}y^{3})^{2}= 2^{2}m^{2\cdot 2}n^{4\cdot 2}y^{3\cdot 2}=4m^{4}n^{8}y^{6}$

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Example Question #37 : Power Rule Of Exponents

Simplify the following:

$({x^{9}})^6$ +(y^3)^4

Possible Answers:

$x^{{15}}+y^{12}$

$x^{{54}}+y^{7}$

$x^{{54}}+y^{12}$

$x^{{15}}+y^{7}$

None of the above

Correct answer:

$x^{{54}}+y^{12}$

Explanation:

When you raise an exponent to an additional power you need to multiply the two numbers, so you will get:

$x^{{9*6}}+y^{3*4}$ which equals $x^{{54}}+y^{12}$

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Example Question #1 : Product Rule Of Exponents

Simplify:

$3x^{2}2y^{7}\times 5x^{5}y^{3}$

Possible Answers:

$30x^{10}y^{21}$

$30x^{7}y^{10}$

$30xy^{17}$

$30x^{17}y$

$15x^{7}2y^{10}$

Correct answer:

$30x^{7}y^{10}$

Explanation:

When multiplying variables with exponents, we must remember the Product Rule of Exponents: $x^{m}*x^{n}=x^{m+n}$

Step 1: Reorganize the terms so the terms are together:

$3x^{2}2y^{7}\times 5x^{5}y^{3} = 3\times2\times5\times x^{2} \times x^{5}\times y^{7} \times y^{3}$

Step 2: Multiply $3\times2\times5$ :

$30\times x^{2}\times x^{5}\times y^{7}\times y^{3}$

Step 3: Use the Product Rule of Exponents to combine $x^{2}$ and $x^{5}$ , and then $y^{3}$ and $y^{7}$ :

$30\times x^{7}\times y^{10}$

$30x^{7}y^{10}$

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Example Question #1 : Product Rule Of Exponents

Simplify the following.

$(x^{2})(x^{5})$

Possible Answers:

$x^{7}$

$x^{-3}$

$x^{10}$

$x^{3}$

Correct answer:

$x^{7}$

Explanation:

The Product of Powers Property states when we multiply two powers with the same base, we add the exponents.

In this case, the exponents are 2 and 5

$x^{2+5}=x^{7}$

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Example Question #2 : Product Rule Of Exponents

Simplify the following expression:

6a^2b(2b^3)

Possible Answers:

8a^2b^3

8a^2 + 8b^4

12a^2b^4

12a^2b^3

Correct answer:

12a^2b^4

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 6a^2b = 6 (a)(a)(b)

And the second term 2b^3 =2(b)(b)(b)

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

First multiply the coefficients, 6(2)=12

We also have a total of 4 's and 2 's all being multipled together.

The final answer is 12a^2b^4

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Example Question #2 : Product Rule Of Exponents

Simplify the following expression:

(-2t^7s)(-5ts^3)

Possible Answers:

-10t^7s^3

10t^8s^4

-7t^8 + s^4

-7t^7s^3

Correct answer:

10t^8s^4

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 -2t^7s = -2(t)(t)(t)(t)(t)(t)(t)(s)

And the second term -5ts^3 = -5(t)(s)(s)(s)

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

First multiply the coefficients, (-2)(-5)=10

We also have a total of 8 's and 4 's all being multipled together.

The final answer is 10t^8s^4

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Pre-Algebra : Polynomials

Study concepts, example questions & explanations for Pre-Algebra

All Pre-Algebra Resources

Example Questions

Example Question #32 : Power Rule Of Exponents

Example Question #33 : Power Rule Of Exponents

Example Question #34 : Power Rule Of Exponents

Example Question #35 : Power Rule Of Exponents

Example Question #36 : Power Rule Of Exponents

Example Question #37 : Power Rule Of Exponents

Example Question #1 : Product Rule Of Exponents

Example Question #1 : Product Rule Of Exponents

Example Question #2 : Product Rule Of Exponents

Example Question #2 : Product Rule Of Exponents

All Pre-Algebra Resources

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