SAT Math : SAT Mathematics

Study concepts, example questions & explanations for SAT Math

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Example Questions

Example Question #55 : Exponents

Solve:

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

Possible Answers:

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

\displaystyle x^{2}

\displaystyle x

\displaystyle 1

Correct answer:

\displaystyle x

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:

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

Example Question #56 : Exponents

Solve:

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

Possible Answers:

\displaystyle x^{11}

\displaystyle x^{4}

\displaystyle x^{7}

\displaystyle x^{18}

Correct answer:

\displaystyle 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:

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

Example Question #57 : Exponents

Solve:

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

Possible Answers:

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

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

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

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

Correct answer:

\displaystyle 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):

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

Example Question #58 : Exponents

Solve:

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

Possible Answers:

\displaystyle x^{27}

\displaystyle x^{6}

\displaystyle x^{12}

\displaystyle x^{36}

Correct answer:

\displaystyle 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:

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

Example Question #59 : Exponents

Solve:

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

Possible Answers:

\displaystyle x^{13}

\displaystyle x^{15}

\displaystyle x^{22}

\displaystyle x^{9}

Correct answer:

\displaystyle 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:

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

Example Question #60 : Exponents

Solve:

\displaystyle x^{5}\cdot x^{5}

Possible Answers:

\displaystyle x

\displaystyle 1

\displaystyle x^{25}

\displaystyle x^{10}

Correct answer:

\displaystyle 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:

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

Example Question #2241 : Sat Mathematics

Simplify:

\displaystyle 4^7*4^{18}

Possible Answers:

\displaystyle 4^{25}

\displaystyle 4^{45}

\displaystyle 4^{106}

\displaystyle 4^{35}

\displaystyle 4^{126}

Correct answer:

\displaystyle 4^{25}

Explanation:

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

\displaystyle 4^7*4^{18}=4^{7+18}=4^{25}

Example Question #2242 : Sat Mathematics

Simplify:

\displaystyle 7^8*5^8

Possible Answers:

\displaystyle 35^{16}

\displaystyle 12^{16}

\displaystyle 35^8

\displaystyle 12^8

\displaystyle 57^8

Correct answer:

\displaystyle 35^8

Explanation:

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

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

Example Question #63 : Exponents

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

For all real \displaystyle a,b,

Evaluate 

Possible Answers:

\displaystyle \frac{1}{100}

\displaystyle 0

\displaystyle 100

The value of  is an undefined quantity.

\displaystyle 1

Correct answer:

\displaystyle 1

Explanation:

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

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

.

Example Question #63 : Exponential Operations

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

For all real \displaystyle a,b,

Evaluate: 

Possible Answers:

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

\displaystyle \frac{1}{10}

\displaystyle 10,000

\displaystyle -10,000

\displaystyle 10

Correct answer:

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

Explanation:

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

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

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

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