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SAT Math : SAT Mathematics

Study concepts, example questions & explanations for SAT Math

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Example Questions

Example Question #55 : Exponents

Solve:

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

Possible Answers:

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

$x^{2}$

Correct answer:

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 (1/2)+(1/2), to get a new exponent of 1:

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

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Example Question #56 : Exponents

Solve:

$x^{9}\cdot x^{2}$

Possible Answers:

$x^{11}$

$x^{4}$

$x^{7}$

$x^{18}$

Correct answer:

$x^{11}$

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 9+2, to get a new exponent of 11:

$x^{9}\cdot x^{2}=x^{9+2}=x^{11}$

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Example Question #57 : Exponents

Solve:

$x^{\frac{1}{5}}\cdot x^{\frac{3}{5}}$

Possible Answers:

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

$x^{\frac{4}{5}}$

$x^{\frac{3}{10}}$

$x^{\frac{3}{25}}$

Correct answer:

$x^{\frac{4}{5}}$

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 (1/5)+(3/5), to get a new exponent of (4/5):

$x^{\frac{1}{5}}\cdot x^{\frac{3}{5}}=x ^{\frac{1}{5}+\frac{3}{5}}=x^{\frac{4}{5}}$

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Example Question #58 : Exponents

Solve:

$x^{3}\cdot x^{9}$

Possible Answers:

$x^{27}$

$x^{6}$

$x^{12}$

$x^{36}$

Correct answer:

$x^{12}$

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+9, to get a new exponent of 12:

$x^{3}\cdot x^{9}=x ^{3+9}=x^{12}$

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Example Question #59 : Exponents

Solve:

$x^{2}\cdot x^{11}$

Possible Answers:

$x^{13}$

$x^{15}$

$x^{22}$

$x^{9}$

Correct answer:

$x^{13}$

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+11, to get a new exponent of 13:

$x^{2}\cdot x^{11}=x ^{2+11}=x^{13}$

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Example Question #60 : Exponents

Solve:

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

Possible Answers:

$x^{25}$

$x^{10}$

Correct answer:

$x^{10}$

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 5+5, to get a new exponent of 10:

$x^{5}\cdot x^{5}=x ^{5+5}=x^{10}$

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Example Question #61 : Exponents

Simplify:

$4^7*4^{18}$

Possible Answers:

$4^{106}$

$4^{35}$

$4^{45}$

$4^{126}$

$4^{25}$

Correct answer:

$4^{25}$

Explanation:

When multiplying exponents, we just add the exponents while keeping the base the same.

$4^7*4^{18}=4^{7+18}=4^{25}$

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Example Question #62 : Exponents

Simplify:

7^8*5^8

Possible Answers:

35^8

$35^{16}$

57^8

$12^{16}$

12^8

Correct answer:

35^8

Explanation:

When multiplying exponents with different bases but the same exponent, you multiply the bases and keep the exponents the same.

7^8*5^8=(7*5)^8=35^8

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Example Question #63 : Exponents

Define an operation $\bigstar$ on the set of real numbers as follows:

For all real a,b ,

$a \bigstar b = a ^{2+ b }$

Evaluate $100 \bigstar (-2)$

Possible Answers:

$\frac{1}{100}$

100

The value of $100 \bigstar (-2)$ is an undefined quantity.

Correct answer:

Explanation:

Set a =100 and b= 2 in the expression in the definition, then simplify the exponent:

$a \bigstar b = a ^{2+ b }$

$100 \bigstar (-2)= 100 ^{2+ (-2)}$

$100 \bigstar (-2)= 100 ^{0}$

Any nonzero number raised to the power of 0 is equal to 1, so

$100 \bigstar (-2)= 1$ .

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Example Question #63 : Exponential Operations

Define an operation $\bigstar$ on the set of real numbers as follows:

For all real a,b ,

$a \bigstar b =\left ( \frac{1}{a} \right )^ {\frac{1}{b}}$

Evaluate: $100 \bigstar \frac{1}{2}$

Possible Answers:

$\frac{1}{10,000}$

$\frac{1}{10}$

10,000

-10,000

Correct answer:

$\frac{1}{10,000}$

Explanation:

Set a =100 and $b= \frac{1}{2}$ in the expression in the definition:

$a \bigstar b =\left ( \frac{1}{a} \right )^ {\frac{1}{b}}$

$100 \bigstar \frac{1}{2 }=\left ( \frac{1}{100} \right )^ {\frac{1}{ \frac{1}{2}}}$

The exponent $\frac{1}{ \frac{1}{2}}$ simplifies as follows:

$\frac{1}{ \frac{1}{2}} = 1 \div \frac{1}{2} = 1 \cdot 2 = 2$ , so

$100 \bigstar \frac{1}{2 }=\left ( \frac{1}{100} \right )^ {2}= \frac{1}{100} \cdot \frac{1}{100} = \frac{1}{10,000}$

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SAT Math : SAT Mathematics

Study concepts, example questions & explanations for SAT Math

All SAT Math Resources

Example Questions

Example Question #55 : Exponents

Example Question #56 : Exponents

Example Question #57 : Exponents

Example Question #58 : Exponents

Example Question #59 : Exponents

Example Question #60 : Exponents

Example Question #61 : Exponents

Example Question #62 : Exponents

Example Question #63 : Exponents

Example Question #63 : Exponential Operations

All SAT Math Resources

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