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SAT Math : SAT Mathematics

Study concepts, example questions & explanations for SAT Math

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Example Questions

Example Question #1 : How To Subtract Exponents

Evaluate 2^9-2^8

Possible Answers:

2^8

2^6

2^7

2^10

Correct answer:

2^8

Explanation:

When subtracting exponents, we don't multiply the exponents but we try to factor to see if we simplify the subtraction problem. In this case, we can simplify it by factoring 2^8 . We get 2^8(2-1)=2^8(1)=2^8 .

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Example Question #2 : How To Subtract Exponents

Evaluate $3^{5}-6^{3}$

Possible Answers:

3^4(2)

3^3

Correct answer:

3^3

Explanation:

Although we have different bases, we know that 6^3=(2*3)^3=2^3*3^3 . As long as exponents are the same, you are allowed to break the base to its prime numbers. Next, we can factor 3^3 . 3^3(3^2-2^3)=27(9-8)=27

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Example Question #517 : Algebra

Evaluate $8^7-2^{20}$

Possible Answers:

-2^5

$6^{13}$

2^8

$2^{20}$

6^4

Correct answer:

$2^{20}$

Explanation:

Although we have different bases, we know that 8=2^3 . Therefore our expression is $(2^3)^7-2^{20}=2^{21}-2^{20}$ . Remember to apply the power rule of exponents. Next, we can factor out $2^{20}.$ We get $2^{20}(2-1)=2^{20}(1)=2^{20}$ .

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Example Question #518 : Algebra

Simplify so that all exponents are positive:

$\frac{x^5 y^3 z^{10}}{x^6 y z^4}$

Possible Answers:

$\frac{x}{y^2z^6}$

$\frac{y^2 z^6}{x}$

$x^{11}y^4z^{14}$

$x^{-1}y^2 z^6$

xy^2z^6

Correct answer:

$\frac{y^2 z^6}{x}$

Explanation:

When we divide two polynomials with exponents, we subtract their exponents.

$\frac{x^5 y^3 z^{10}}{x^6 y z^4} = x^{5-6}y^{3-1}z^{10-4} = x^{-1}y^2z^6$

Remember that the question asks that all exponents be positive numbers. Therefore:

$x^{-1}y^2z^6 = \frac{y^2z^6}{x}$

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Example Question #2 : How To Subtract Exponents

Evaluate:

$2^{10}-2^9$

Possible Answers:

2^9

$2^{9.5}$

2^8

$2^{-9}$

2^6

Correct answer:

2^9

Explanation:

When subtracting with exponents, we try to factor out some terms.

We can factor out 2^9 to get

2^9(2-1)=2^9*1=2^9 .

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Example Question #101 : Exponents

Evaluate:

$3^{14}-3^{13}-3^{13}$

Possible Answers:

$3^{-12}$

$3^{12}$

3^9

$3^{11}$

$3^{13}$

Correct answer:

$3^{13}$

Explanation:

When subtracting with exponents, we try to factor out some terms.

We can factor out $3^{13}$ to get

$3^{13}(3-1-1)=3^{13}*(1)=3^{13}$ .

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Example Question #111 : Exponents

Simplify:

$4^8-2^{15}$

Possible Answers:

$2^{14}$

$2^{15}$

$2^{-7}$

$2^{20}$

Correct answer:

$2^{15}$

Explanation:

Although we have different bases, we know that 4=2^2 .

Therefore,

$4^8=(2^2)^8=2^{16}$ .

Finally, we factor out $2^{15}$ to get

$2^{15}(2-1)=2^{15}*1=2^{15}$ .

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Example Question #2 : How To Subtract Exponents

If $x\star y=x^2-y^2$ , then what is $4\star (5\star 3)$ ?

Possible Answers:

240

Correct answer:

Explanation:

$4\star (5\star 3)$

Follow the order of operations by solving the expression within the parentheses first.

$x\star y=x^2-y^2$

$5\star 3=(5)^2-(3)^2$

$5\star 3=25-9=16$

Return to solve the original expression.

$4\star(5\star3)=4\star(16)$

$x\star y=x^2-y^2$

$4\star16=(4)^2-(16)^2$

$4\star(16)=-240$

$4\star(5\star3)=-240$

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Example Question #1 : How To Divide Exponents

For all real numbers n, (2ⁿ * 2) / (2ⁿ * 2ⁿ) =

Possible Answers:

2^{1 – n}

2n/2n

2n – 1

Correct answer:

2^{1 – n}

Explanation:

(2ⁿ * 2) / (2ⁿ * 2ⁿ) simplifies to 2/2ⁿ or 2¹/2ⁿ.

When dividing exponents with the same base, you subtract the divisor from the dividend, giving 2^1–n.

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Example Question #113 : Exponents

If x⁹/x³ = xⁿ, solve for n.

Possible Answers:

Correct answer:

Explanation:

When dividing terms with the same base, we can subtract the exponents:

9 – 3 = 6

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SAT Math : SAT Mathematics

Study concepts, example questions & explanations for SAT Math

All SAT Math Resources

Example Questions

Example Question #1 : How To Subtract Exponents

Example Question #2 : How To Subtract Exponents

Example Question #517 : Algebra

Example Question #518 : Algebra

Example Question #2 : How To Subtract Exponents

Example Question #101 : Exponents

Example Question #111 : Exponents

Example Question #2 : How To Subtract Exponents

Example Question #1 : How To Divide Exponents

Example Question #113 : Exponents

All SAT Math Resources

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