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PSAT Math : Exponential Operations

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Example Questions

Example Question #121 : Exponential Operations

$\frac{55^{10}}{121^6} \cdot \frac{11^8}{5^{8}} = ?$

Possible Answers:

$605^{4}$

$5^2\cdot11^6$

11^6

$\frac{5^2}{11^4}$

$\frac{5^{18}}{11^4}$

Correct answer:

$5^2\cdot11^6$

Explanation:

The key to this problem is understanding how exponents divide. When two exponents have the same base, then the exponent on the bottom can simply be subtracted from the exponent on top. I.e.:

$\frac{5^x}{5^y} = 5^{x-y}$

Keeping this in mind, we simply break the problem down into prime factors, multiply out the exponents, and solve.

$\frac{55^{10}}{121^6} \cdot \frac{11^8}{5^8} = \frac{(5\cdot 11)^{10}}{5^8}\cdot \frac{11^8}{(11\cdot11)^6} = 11^{10}\cdot\frac{5^{10}}{5^8} \cdot \frac{11^8}{11^{12}} = 5^2 \cdot \frac{11^{10+8}}{11^{12}} = 5^2\cdot11^6$

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Example Question #2 : How To Divide Exponents

Simplify

$\dpi{100} \small \frac{20x^{4}y^{-3}z^{2}}{5z^{-1}y^{2}x^{2}}=$

Possible Answers:

$\dpi{100} \small {4x^{5}y^{-2}}$

$\dpi{100} \small \frac{4x^{2}z^{3}}{y^{5}}$

$\dpi{100} \small 15x^{-2}y^{-2}z^{-2}$

None

$\dpi{100} \small 15x^{2}y^{2}z^{2}$

Correct answer:

$\dpi{100} \small \frac{4x^{2}z^{3}}{y^{5}}$

Explanation:

Divide the coefficients and subtract the exponents.

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Example Question #3 : How To Divide Exponents

Which of the following is equal to the expression Equationgre , where

xyz ≠ 0?

Possible Answers:

1/y

z/(xy)

xyz

Correct answer:

1/y

Explanation:

(xy)⁴ can be rewritten as x⁴y⁴ and z⁰ = 1 because a number to the zero power equals 1. After simplifying, you get 1/y.

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Example Question #4 : How To Divide Exponents

If $c\neq 0$ , then $\frac{(c^3)^2}{c^2c^4}=?$

Possible Answers:

c^4

Cannot be determined

c^2

Correct answer:

Explanation:

Start by simplifying the numerator and denominator separately. In the numerator, (c³)² is equal to c⁶. In the denominator, c²* c⁴ equals c⁶ as well. Dividing the numerator by the denominator, c⁶/c⁶, gives an answer of 1, because the numerator and the denominator are the equivalent.

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Example Question #11 : How To Divide Exponents

If $a\not\equiv0$ , which of the following is equal to $\frac{(a^6*a^2)^3}{a^6}$ ?

Possible Answers:

a⁴

a¹⁸

The answer cannot be determined from the above information

a⁶

Correct answer:

a¹⁸

Explanation:

The numerator is simplified to a^8 (by adding the exponents), then cube the result. a²⁴/a⁶ can then be simplified to $a^{18}$ .

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Example Question #2 : Exponential Operations

$\dpi{100} \small \frac{7^{10}-7^{8}}{7^{9}-7^{7}}=$

Possible Answers:

$\dpi{100} \small 28$

$\dpi{100} \small 49$

$\dpi{100} \small 343$

$\dpi{100} \small 42$

$\dpi{100} \small 7$

Correct answer:

$\dpi{100} \small 7$

Explanation:

The easiest way to solve this is to simplify the fraction as much as possible. We can do this by factoring out the greatest common factor of the numerator and the denominator. In this case, the GCF is 7^7 .

$\frac{7^7\left ( 7^3-7^1\right)}{7^7\left ( 7^2-1\right)}$

Now, we can cancel out the 7^7 from the numerator and denominator and continue simplifying the expression.

$\frac{7^7\left ( 7^3-7^1\right)}{7^7\left ( 7^2-1\right)}=\frac{7^3-7^1}{7^2-1}=\frac{343-7}{49-1}=\frac{336}{48}=7$

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Example Question #1 : Exponents

If (300)(400) = 12 * 10ⁿ, n =

Possible Answers:

Correct answer:

Explanation:

(300)(400) = 120,000 or 12 * 10⁴.

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Example Question #1 : Exponents

(2x10³) x (2x10⁶) x (2x10¹²) = ?

Possible Answers:

6x10²¹

8x10²¹

6x10²³

8x10²³

Correct answer:

8x10²¹

Explanation:

The three two multiply to become 8 and the powers of ten can be added to become 10²¹.

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Example Question #1 : How To Multiply Exponents

Which of the following is equivalent to (3x^4)(2x^2)

Possible Answers:

6x^6

6x^8

5x^6

5x^8

Correct answer:

6x^6

Explanation:

and can be multiplied together to give you which is the first part of our answer. When you multiply exponents with the same base (in this case, ), you add the exponents. In this case, $x^4\times x^2$ should give us x^6 because 4+2=6 . The answer is 6x^6

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Example Question #1 : How To Multiply Exponents

If 3^x = 27, then 2^2x= ?

Possible Answers:

Correct answer:

Explanation:

Solve for x in 3^x = 27. x = 3 because 3 * 3 * 3 = 27.
Since x = 3, one can substitute x for 3 in 2^2x
Now, the expression is 2^2*3
This expression can be interpreted as 2^{2 *}2²* 2². Since 2²= 4, the expression can be simplified to become 4 * 4 * 4 = 64.
You can also multiply the powers to simplify the expression. When you multiply the powers, you get 2⁶, or 2 * 2 * 2 * 2 * 2 * 2
2⁶= 64.

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PSAT Math : Exponential Operations

Study concepts, example questions & explanations for PSAT Math

All PSAT Math Resources

Example Questions

Example Question #121 : Exponential Operations

Example Question #2 : How To Divide Exponents

Example Question #3 : How To Divide Exponents

Example Question #4 : How To Divide Exponents

Example Question #11 : How To Divide Exponents

Example Question #2 : Exponential Operations

Example Question #1 : Exponents

Example Question #1 : Exponents

Example Question #1 : How To Multiply Exponents

Example Question #1 : How To Multiply Exponents

All PSAT Math Resources

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