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SAT Math : SAT Mathematics

Study concepts, example questions & explanations for SAT Math

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16 Diagnostic Tests 660 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #41 : Exponents

Evaluate $6^{18}*6^{24}$

Possible Answers:

$6^{48}$

$6^{24}$

$6^{36}$

$6^{432}$

$6^{42}$

Correct answer:

$6^{42}$

Explanation:

When multiplying exponents of the same base, we just add the exponents and keep the base the same.

$6^{18}*6^{24}=6^{18+24}=6^{42}$

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Example Question #42 : Exponents

Evaluate $7^{-5}*7^{-8}$

Possible Answers:

$7^{-10}$

$7^{16}$

$7^{40}$

$7^{-12}$

$7^{-13}$

Correct answer:

$7^{-13}$

Explanation:

When multiplying exponents of the same base, we just add the exponents and keep the base the same.

$7^{-5}*7^{-8}=7^{-5-8}=7^{-13}$

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Example Question #43 : Exponents

Evaluate 81^8*3^9

Possible Answers:

$243^{17}$

$3^{41}$

9^9

$243^{72}$

$3^{80}$

Correct answer:

$3^{41}$

Explanation:

Although we have different bases, we know that 81=3^4. Therefore we have $(3^4)^8*3^9=3^{32}*3^9=3^{41}$ .

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Example Question #42 : How To Multiply Exponents

Simplify $\frac{x+(3x)^2+(2x)^3}{x}$

Possible Answers:

x+9x^2+8x^3

1+9x+8x^2

$\frac{1+9x+8x^2}{x}$

1+6x+6x^2

x+9x+8x^2

Correct answer:

1+9x+8x^2

Explanation:

Simplify the numerator

$\frac{x+(3x)^2+(2x)^3}{x}=\frac{x+3^2x^2+2^3x^3}{x}=\frac{x+9x^2+8x^3}{x}$

Pull an x out of each term in the numerator

$\frac{x(1+9x+8x^2)}{x}$

The x in the numerator and the x in the denominator cancel

1+9x+8x^2

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Example Question #45 : Exponents

Solve:

$x^{6}\cdot x^{12}$

Possible Answers:

$x^{18}$

$x^{6}$

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

$x^{2}$

Correct answer:

$x^{18}$

Explanation:

When multiplying expressions with the same variable, combine terms by adding the exponents, while leaving the variable unchanged. For this problem, we do that by adding 6+12, to get a new exponent of 18:

$x^{6}\cdot x^{12}=x ^{6+12}=x^{18}$

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Example Question #46 : Exponents

Solve:

$x^{2}\cdot x$

Possible Answers:

$x^{2}$

$x^{5}$

$x^{3}$

Correct answer:

$x^{3}$

Explanation:

When multiplying expressions with the same variable, combine terms by adding the exponents, while leaving the variable unchanged. For this problem, we do that by adding 2+1, to get a new exponent of 3:

$x^{2}\cdot x=x ^{2+1}=x^{3}$

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Example Question #461 : Algebra

Solve:

$x\cdot x^{3}$

Possible Answers:

$x^{4}$

$x^{2}$

$x^{5}$

$x^{3}$

Correct answer:

$x^{4}$

Explanation:

When multiplying expressions with the same variable, combine terms by adding the exponents, while leaving the variable unchanged. For this problem, we do that by adding 3+1, to get a new exponent of 4:

$x^{3}\cdot x=x ^{3+1}=x^{4}$

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Example Question #462 : Algebra

Solve:

$x^{2}\cdot x^{5}$

Possible Answers:

$x^{10}$

$x^{7}$

$x^{6}$

$x^{3}$

Correct answer:

$x^{7}$

Explanation:

When multiplying expressions with the same variable, combine terms by adding the exponents, while leaving the variable unchanged. For this problem, we do that by adding 2+5, to get a new exponent of 7:

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

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Example Question #53 : Exponents

Solve:

$x^{4}\cdot x^{2}$

Possible Answers:

$x^{2}$

$x^{6}$

$x^{12}$

$x^{8}$

Correct answer:

$x^{6}$

Explanation:

When multiplying expressions with the same variable, combine terms by adding the exponents, while leaving the variable unchanged. For this problem, we do that by adding 4+2, to get a new exponent of 6:

$x^{4}\cdot x^{2}=x ^{4+2}=x^{6}$

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Example Question #54 : Exponents

Solve:

$x^{3}\cdot x^{5}$

Possible Answers:

$x^{8}$

$x^{6}$

$x^{15}$

$x^{2}$

Correct answer:

$x^{8}$

Explanation:

When multiplying expressions with the same variable, combine terms by adding the exponents, while leaving the variable unchanged. For this problem, we do that by adding 3+5, to get a new exponent of 8:

$x^{3}\cdot x^{5}=x ^{3+5}=x^{8}$

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SAT Math : SAT Mathematics

Study concepts, example questions & explanations for SAT Math

All SAT Math Resources

Example Questions

Example Question #41 : Exponents

Example Question #42 : Exponents

Example Question #43 : Exponents

Example Question #42 : How To Multiply Exponents

Example Question #45 : Exponents

Example Question #46 : Exponents

Example Question #461 : Algebra

Example Question #462 : Algebra

Example Question #53 : Exponents

Example Question #54 : Exponents

All SAT Math Resources

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