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Pre-Algebra : Polynomials

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Example Questions

Example Question #25 : Product Rule Of Exponents

Simplify:

(x^2y)(x^4y^3)

Possible Answers:

$\frac{1}{x^2y^2}$

x^6y^4

x^7y^2

x^8y^3

Correct answer:

x^6y^4

Explanation:

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

(x^2y)(x^4y^3)=x^6y^4

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Example Question #26 : Product Rule Of Exponents

Simplify:

(f^5)(f^5)

Possible Answers:

$f^{10}$

f^5

$f^{25}$

Correct answer:

$f^{10}$

Explanation:

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

$(f^5)(f^5)=f^{10}$

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Example Question #27 : Product Rule Of Exponents

Simplify:

(g^2h^8)(g^6h^6)

Possible Answers:

$g^8h^{48}$

$\frac{h^2}{g^4}$

$g^{12}h^{14}$

$g^8h^{14}$

Correct answer:

$g^8h^{14}$

Explanation:

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

$(g^2h^8)(g^6h^6)=g^8h^{14}$

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Example Question #28 : Product Rule Of Exponents

Simplify:

$(i^{12})(i^{-4})$

Possible Answers:

i^8

i^9

i^3

$i^{16}$

Correct answer:

i^8

Explanation:

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

$(i^{12})(i^{-4})=i^8$

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Example Question #29 : Product Rule Of Exponents

Simplify:

(u^2t^7)(u^7t^5)

Possible Answers:

$u^7t^{10}$

$u^{12}t^9$

$u^9t^{12}$

$\frac{u^2}{t^5}$

Correct answer:

$u^9t^{12}$

Explanation:

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

$(u^2t^7)(u^7t^5)=u^9t^{12}$

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Example Question #126 : Polynomials

Simplify: $(a^{2}b^{-2})^{-2}$

Possible Answers:

b^2

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

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

b^4

Correct answer:

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

Explanation:

According to the power rule for exponents, if a quantity is raised to a certain exponent, the powers of the inner quantity can be multiplied with the power outside the parentheses.

$(a^{2}b^{-2})^{-2} = a^{-4} b^{4}$

Eliminate the negative exponent by the following rule:

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

$a^{-4} b^{4} = \frac{b^{4}}{a^{4}}$

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Example Question #31 : Product Rule Of Exponents

Simplify: $4^2 \cdot 4^{-5} \cdot 4^{10}$

Possible Answers:

4^7

$4^{-7}$

$4^{-4}$

4^4

$4^{-3}$

Correct answer:

4^7

Explanation:

Since the bases are all alike and are multiplied, the exponents can be added.

In mathematical terms:

$a^n\cdot a^m=a^{n+m}$

Plugging in four as our base and the various exponents we get the following,

$4^2 \cdot 4^{-5} \cdot 4^{10} = 4^{2-5+10} = 4^7$ .

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Example Question #32 : Product Rule Of Exponents

Expand: (3x^3)^3

Possible Answers:

27 x^6

3x^9

9x^9

3x^6

27 x^9

Correct answer:

27 x^9

Explanation:

The exponents can be multiplied in this case.

Expand out the terms to verify.

(3x^3)^3 = (3x^3)(3x^3)(3x^3) = 27 x^9

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Example Question #33 : Product Rule Of Exponents

Solve: 3(a^2)^3 + (3a^2)^3

Possible Answers:

27a^6

12a^6

30a^6

6a^6

9a^6

Correct answer:

30a^6

Explanation:

Evaluate the quantities inside the parentheses first. The powers are multiplied when they are bounded in the parentheses.

3(a^2)^3 + (3a^2)^3 = 3a^6 + 3^3(a^6)

3a^6 + 3^3(a^6) = 3a^6 + 27a^6

Combine like-terms.

3a^6 + 27a^6 = 30a^6

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Example Question #130 : Polynomials

Evaluate:

$(a^2)^4\cdot(a^{-2})^3$

Possible Answers:

$a^{24}$

$\frac{1}{a^2}$

a^2

Correct answer:

a^2

Explanation:

Simplify each parentheses before multiplying.

Recall the rules of exponents which states if exponents are being raised to another one they are multiplied and if like bases are being multiplied their exponents are added.

$(a^n)^m=a^{n\cdot m}$

$a^n\cdot a^m=a^{n+m}$

Applying these rules we get,

$(a^2)^4\cdot(a^{-2})^3 = a^8 \cdot a^{-6} = a^{8+(-6)}=a^2$ .

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Pre-Algebra : Polynomials

Study concepts, example questions & explanations for Pre-Algebra

All Pre-Algebra Resources

Example Questions

Example Question #25 : Product Rule Of Exponents

Example Question #26 : Product Rule Of Exponents

Example Question #27 : Product Rule Of Exponents

Example Question #28 : Product Rule Of Exponents

Example Question #29 : Product Rule Of Exponents

Example Question #126 : Polynomials

Example Question #31 : Product Rule Of Exponents

Example Question #32 : Product Rule Of Exponents

Example Question #33 : Product Rule Of Exponents

Example Question #130 : Polynomials

All Pre-Algebra Resources

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