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Pre-Algebra : Product Rule of Exponents

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Example Questions

Example Question #21 : Product Rule Of Exponents

Simplify:

$(a^7)(a^{-4})$

Possible Answers:

a^3

a^2

$a^{-3}$

$a^{11}$

Correct answer:

a^3

Explanation:

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

$(a^7)(a^{-4})=a^3$

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Example Question #22 : Product Rule Of Exponents

Simplify:

$(b^5)(b^{-4})$

Possible Answers:

b^9

$\frac{1}{b}$

b^2

Correct answer:

Explanation:

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

$(b^5)(b^{-4})=b$

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Example Question #23 : Product Rule Of Exponents

Simplify:

(c^6)(c)

Possible Answers:

c^8

c^6

c^7

c^5

Correct answer:

c^7

Explanation:

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

(c^6)(c)=c^7

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Example Question #24 : Product Rule Of Exponents

Simplify:

$(d^{13})(d^6)$

Possible Answers:

$d^{19}$

$d^{14}$

d^5

d^7

Correct answer:

$d^{19}$

Explanation:

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

$(d^{13})(d^6)=d^{19}$

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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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Pre-Algebra : Product Rule of Exponents

Study concepts, example questions & explanations for Pre-Algebra

All Pre-Algebra Resources

Example Questions

Example Question #21 : Product Rule Of Exponents

Example Question #22 : Product Rule Of Exponents

Example Question #23 : Product Rule Of Exponents

Example Question #24 : Product Rule Of Exponents

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

All Pre-Algebra Resources

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