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Pre-Algebra : Polynomials

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Example Questions

Example Question #81 : Polynomials

Solve: 3x^4+3x^2(2x^2)

Possible Answers:

9x^8

9x^6

9x^4

3x^4+6x^6

3x^4+6x^2

Correct answer:

9x^4

Explanation:

Solve by eliminating the parentheses first. When powers of the same base are multiplied, the powers can be added.

$3x^4+3x^2(2x^2) = 3x^4+ 6x^{2+2}= 3x^4+6x^4$

Combine like-terms.

3x^4+6x^4 =9x^4

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Example Question #82 : Polynomials

Solve: $(-a)(a^4) + 2a^2\times a^4$

Possible Answers:

2a^8-a^5

2a^6-a^3

2a^6-a^4

2a^6-a^5

2a^8-a^4

Correct answer:

2a^6-a^5

Explanation:

Solve the parentheses first.

(-a)(a^4) = -a^5

Simplify the third and fourth terms.

$2a^2\times a^4 = 2a^6$

Combine or add the two terms.

2a^6-a^5

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Example Question #82 : Polynomials

Solve: $\frac{a^4\times a^{-3}}{a^{-4}}$

Possible Answers:

a^5

$\frac{1}{a^3}$

$\frac{1}{a^4}$

a^3

Correct answer:

a^5

Explanation:

Simplify the numerator first.

$\frac{a^4\times a^{-3}}{a^{-4}} = \frac{a^{4+(-3)}}{a^{-4}} =\frac{a}{a^{-4}}$

When dividing similar bases, their powers can be subtracted.

$\frac{a}{a^{-4}} = a^{1-(-4)}=a^5$

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Example Question #84 : Polynomials

Solve: $2b^2\cdot 3b^{-9}$

Possible Answers:

$-\frac{6 }{b^7}$

$6b^{\frac{2}{9}}$

$\large 6b^{\frac{9}{2}}$

$\frac{6}{b^7}$

$\frac{6}{b^{18}}$

Correct answer:

$\frac{6}{b^7}$

Explanation:

When similar bases are multiplied, their powers can be added together.

$2b^2\cdot 3b^{-9} = 2\cdot 3 \cdot b^{2+(-9)} = 6b^{-7}$

The next step is to eliminate the negative exponent.

Remember that a value to a negative power is one over that value to its positive power. Write the following rule:

$x^{-n} = \frac{1}{x^n}$

Apply this rule for $6b^{-7}$ .

$6b^{-7} = 6 \cdot \frac{1}{b^7}$

Multiply the whole number with the numerator.

$6\cdot \frac{1}{b^7}= \frac{6}{b^7}$

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Example Question #85 : Polynomials

Solve the following expression: $a^2b^4\cdot b^{-3}c^3 \cdot a^{-1}$

Possible Answers:

a^3b^3c^3

$\frac{ac^3}{b^{12}}$

$\frac{c^3}{a^2b^{12}}$

a^3b^7c^3

abc^3

Correct answer:

abc^3

Explanation:

Since every base of a certain power is all multiplied, the powers of the similar bases can be added.

Reorganize the terms.

$a^2b^4\cdot b^{-3}c^3 \cdot a^{-1} = a^2 \cdot a^{-1}\cdot b^4 \cdot b^{-3}\cdot c^3$

Simplify the bases.

$a^2 \cdot a^{-1}\cdot b^4 \cdot b^{-3}\cdot c^3 = a^{2+(-1)}b^{4+(-3)}c^3$

Add the powers to get the answer.

$a^{2+(-1)}b^{4+(-3)}c^3 = abc^3$

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Example Question #86 : Polynomials

How do I make the following equation have a positive exponent?

7^-^5

Possible Answers:

7^5

$\frac{1}{7^5}$

$\frac{7^5}{1}$

$\frac{1}{35}$

Correct answer:

$\frac{1}{7^5}$

Explanation:

When solving a negative exponent question simply do the reciprocal of the fraction and change the sign of the exponent.

7^-^5 is really $\frac{7^-^5}{1}$ .

Recipricol means flip, so;

$\frac{1}{7^-^5}$

Then change the sign of the exponent.

$\frac{1}{7^5}$

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Example Question #87 : Polynomials

Simplify: $\frac{21^8}{7^2}$

Possible Answers:

3^1^0

28^6

3^6

3^4

14^1^0

Correct answer:

3^6

Explanation:

When solving a division exponent question if the base is the same take it to the answer and then subtract the exponents.

In this case the bases are different so you must divide the bases then subtract the exponents.

$\frac{21^8}{7^2}$

Divide the bases: $\frac{21}{7} = 3$

Subtract the exponents: 8 - 2 = 6

The answer is 3^6

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Example Question #83 : Polynomials

Find the solution to the equation.

(23^5)^7

Possible Answers:

115^7

23^2

23^-^2

23^3^5

23^1^2

Correct answer:

23^3^5

Explanation:

When an exponent question is in this product form we need to multiply the exponents together.

23^5^ ^* ^7 = 23^3^5

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Example Question #89 : Polynomials

Solve the following

(a^3)^4

Possible Answers:

$a^{7}$

a^4

$a^{1}$

$a^{34}$

$a^{12}$

Correct answer:

$a^{12}$

Explanation:

When you raise a power to a power, you multiply the two powers together. So,

$(a^3)^4 = a^{3 \cdot 4} = a^{12}$

We can also look at it like this:

$(a^3)^4 = a^3 \cdot a^3 \cdot a^3 \cdot a^3$

$(a^3)^4 = a \cdot a \cdot a \cdot a \cdot a \cdot a \cdot a \cdot a \cdot a \cdot a \cdot a \cdot a$

$(a^3)^4 = a^{12}$

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Example Question #84 : Polynomials

Simplify the following

(a^4)^2

Possible Answers:

$a^{42}$

a^2

a^8

a^6

a^4

Correct answer:

a^8

Explanation:

When you have the same base and you raise a power to a power, you multiply the exponents. So,

$(a^4)^2 = a^{4 \cdot 2} = a^8$

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Pre-Algebra : Polynomials

Study concepts, example questions & explanations for Pre-Algebra

All Pre-Algebra Resources

Example Questions

Example Question #81 : Polynomials

Example Question #82 : Polynomials

Example Question #82 : Polynomials

Example Question #84 : Polynomials

Example Question #85 : Polynomials

Example Question #86 : Polynomials

Example Question #87 : Polynomials

Example Question #83 : Polynomials

Example Question #89 : Polynomials

Example Question #84 : Polynomials

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