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SAT Math : SAT Mathematics

Study concepts, example questions & explanations for SAT Math

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Example Questions

Example Question #8 : Exponential Operations

If $\frac{3^{y - 1}}{3^{-2}} = 27^{y}3^{y}$ , what is the value of ?

Possible Answers:

$\frac{1}{3}$

$\frac{2}{3}$

$\frac{3}{2}$

Correct answer:

$\frac{1}{3}$

Explanation:

Rewrite the term on the left as a product. Remember that negative exponents shift their position in a fraction (denominator to numerator).

$3^{y-1}*3^2=27^y3^y$

The term on the right can be rewritten, as 27 is equal to 3 to the third power.

$3^{y-1}*3^2=(3^3)^y*3^y$

Exponent rules dictate that multiplying terms allows us to add their exponents, while one term raised to another allows us to multiply exponents.

$3^{(y-1)+2}=(3)^{3y}*3^y$

$3^{y+1}=3^{3y+y}=3^{4y}$

We now know that the exponents must be equal, and can solve for .

y+1=4y

1=3y

$\frac{1}{3}=y$

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Example Question #84 : Exponents

If $5^2 \times 5^n = 5^{12}$ , what is the value of ?

Possible Answers:

Correct answer:

Explanation:

Since the base is 5 for each term, we can say 2 + n =12. Solve the equation for n by subtracting 2 from both sides to get n = 10.

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Example Question #86 : Exponential Operations

Simplify: $3^2\times3^3\times3^{-4}$

Possible Answers:

$\frac{1}{3}$

$\frac{1}{9}$

Correct answer:

Explanation:

To determine the value of this expression, it is not necessary to determine the values of each term's power. Instead, since these powers have the same bases and are multiplied, the powers can be added.

$3^2\times3^3\times3^{-4} = 3^{2+3+(-4)} = 3^1=3$

The answer is .

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Example Question #16 : How To Add Exponents

If $y = 5^{a} * 5^{b}$ and a + b = 3 , what is the value of ?

Possible Answers:

125

150

Correct answer:

125

Explanation:

Multiplying two exponents that have the same base is the equivalent of simply adding the exponents.

So $y = 5^{a} * 5^{b}$ is the same as $y = 5^{a + b}$ , and if a + b = 3 , then $y = 5^{3}$ or 125 .

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Example Question #87 : Exponents

Evaluate: 3^x+9^x

Possible Answers:

$3^{3x}$

$3^{x^2}$

$3^x+3^{2x}$

12^x

Correct answer:

$3^x+3^{2x}$

Explanation:

The exponents cannot be added unless the both bases are alike and similar bases must be multiplied with each other. Rewrite the nine with a base of three.

9=3^2

Rewrite the expression.

$3^x+9^x= 3^x+3^{2x}$

Do not add the exponents, since similar bases are added and are not multiplied with each other!

The answer is: $3^x+3^{2x}$

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Example Question #83 : Exponents

Simplify:

$x^5y^4z^2 \cdot x^4y^5z^2$

Possible Answers:

$xy^{-1}$

x^9y^9z^4

$\frac{x^5y^4z^2 }{x^4y^5z^2}$

$x^{20}y^{20}z^{4}$

Correct answer:

x^9y^9z^4

Explanation:

When we multiply two polynomials with exponents, we add their exponents together. Therefore,

$x^5y^4z^2 \cdot x^4y^5z^2 = x^9y^9z^4$

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Example Question #2271 : Sat Mathematics

Evaluate 3^7+3^7+3^7

Possible Answers:

$3^{21}$

3^8

$3^{27}$

$3^{14}$

$3^{10}$

Correct answer:

3^8

Explanation:

When adding exponents, we don't multiply the exponents but we try to factor to see if we simplify the addition problem. In this case, we can simplify it by factoring 3^7 . We get 3^7(1+1+1)=3^7(3)=3^8 .

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Example Question #2272 : Sat Mathematics

Evaluate 5^7+5^7+5^7+5^7+5^7

Possible Answers:

$5^{40}$

$5^{35}$

$5^{60}$

5^9

5^8

Correct answer:

5^8

Explanation:

When adding exponents, we don't multiply the exponents but we try to factor to see if we simplify the addition problem. In this case, we can simplify it by factoring 5^7 . We get 5^7(1+1+1+1+1)=5^7(5)=5^8 .

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Example Question #23 : How To Add Exponents

Evaluate $2^{12}+4^6$

Possible Answers:

$2^{15}(3)$

4^7(3)

$2^{13}$

$2^{12}(5)$

$4^{12}$

Correct answer:

$2^{13}$

Explanation:

Although we have different bases, we do know 4=2^2 . Therefore our expression is $2^{12}+(2^2)^6=2^{12}+2^{12}$ . Remember to apply the power rule of exponents. Then, now we can factor $2^{12}$ . $2^{12}+2^{12}=2^{12}(1+1)=2^{12}(2)=2^{13}$

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Example Question #2273 : Sat Mathematics

If $\dpi{100} \small r$ and $\dpi{100} \small s$ are positive integers, and $\dpi{100} \small 25\left ( 5^{r} \right )=5^{s-2}$ , then what is $\dpi{100} \small s$ in terms of $\dpi{100} \small r$ ?

Possible Answers:

$\dpi{100} \small r+3$

$\dpi{100} \small r$

$\dpi{100} \small r+2$

$\dpi{100} \small r+1$

$\dpi{100} \small r+4$

Correct answer:

$\dpi{100} \small r+4$

Explanation:

$\dpi{100} \small 25\left ( 5^{r} \right )$ is equal to $5^{2}\left ( 5^{r}\right )$ which is equal to $\dpi{100} \small \left ( 5^{r+2} \right )$ . If we compare this to the original equation we get $\dpi{100} \small r+2=s-2\rightarrow s=r+4$

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SAT Math : SAT Mathematics

Study concepts, example questions & explanations for SAT Math

All SAT Math Resources

Example Questions

Example Question #8 : Exponential Operations

Example Question #84 : Exponents

Example Question #86 : Exponential Operations

Example Question #16 : How To Add Exponents

Example Question #87 : Exponents

Example Question #83 : Exponents

Example Question #2271 : Sat Mathematics

Example Question #2272 : Sat Mathematics

Example Question #23 : How To Add Exponents

Example Question #2273 : Sat Mathematics

All SAT Math Resources

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