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SSAT Upper Level Math : How to find the properties of an exponent

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Example Questions

Example Question #2 : Expressions & Equations

Evaluate $\dpi{100} \frac{2^{10}}{2^{8}}$ $\displaystyle \dpi{100} \frac{2^{10}}{2^{8}}$

Possible Answers:

$\dpi{100} \frac{8}{5}$ $\displaystyle \dpi{100} \frac{8}{5}$

$\dpi{100} 2$ $\displaystyle \dpi{100} 2$

$\dpi{100} 200$ $\displaystyle \dpi{100} 200$

$\dpi{100} 4$ $\displaystyle \dpi{100} 4$

Correct answer:

$\dpi{100} 4$ $\displaystyle \dpi{100} 4$

Explanation:

If you divide two exponential expressions with the same base, you can simply subtract the exponents. Here, both the top and the bottom have a base of 2 raised to a power.

So $\dpi{100} \frac{2^{10}}{2^{8}}=2^{10-8}=2^{2}=4$ $\displaystyle \dpi{100} \frac{2^{10}}{2^{8}}=2^{10-8}=2^{2}=4$

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Example Question #2 : How To Find The Properties Of An Exponent

$\dpi{100} 2^{3}\cdot 2^{2}$ $\displaystyle \dpi{100} 2^{3}\cdot 2^{2}$

Possible Answers:

$\dpi{100} 16$ $\displaystyle \dpi{100} 16$

$\dpi{100} 2^{6}$ $\displaystyle \dpi{100} 2^{6}$

$\dpi{100} 32$ $\displaystyle \dpi{100} 32$

Correct answer:

$\dpi{100} 32$ $\displaystyle \dpi{100} 32$

Explanation:

Since the two expressions have the same base, we just add the exponents.

$\dpi{100} 2^{3}\cdot 2^{2}=2^{3+2}=2^{5}=32$ $\displaystyle \dpi{100} 2^{3}\cdot 2^{2}=2^{3+2}=2^{5}=32$

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Example Question #1 : How To Find The Properties Of An Exponent

Evaluate: $\dpi{100} (3^{3})^{2}$ $\displaystyle \dpi{100} (3^{3})^{2}$

Possible Answers:

$\dpi{100} 3^{6}$ $\displaystyle \dpi{100} 3^{6}$

$\dpi{100} 3^{5}$ $\displaystyle \dpi{100} 3^{5}$

$\dpi{100} 243$ $\displaystyle \dpi{100} 243$

$\dpi{100} 729$ $\displaystyle \dpi{100} 729$

Correct answer:

$\dpi{100} 3^{6}$ $\displaystyle \dpi{100} 3^{6}$

Explanation:

A power raised to a power indicates that you multiply the two powers.

$\dpi{100} (3^{3})^{2}=3^{3\cdot 2}=3^{6}$ $\displaystyle \dpi{100} (3^{3})^{2}=3^{3\cdot 2}=3^{6}$

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Example Question #1 : Properties Of Exponents

$\dpi{100} Evaluate: (0.50^{2})$ $\displaystyle \dpi{100} Evaluate: (0.50^{2})$

Possible Answers:

$\dpi{100} 1$ $\displaystyle \dpi{100} 1$

$\dpi{100} 25$ $\displaystyle \dpi{100} 25$

$\dpi{100} 0.25$ $\displaystyle \dpi{100} 0.25$

$\dpi{100} 2.5$ $\displaystyle \dpi{100} 2.5$

Correct answer:

$\dpi{100} 0.25$ $\displaystyle \dpi{100} 0.25$

Explanation:

We can either write $\dpi{100} 0.5\times 0.5$ $\displaystyle \dpi{100} 0.5\times 0.5$, or we can convert this to a fraction and write

$\dpi{100} \frac{1}{2}\times \frac{1}{2}$ $\displaystyle \dpi{100} \frac{1}{2}\times \frac{1}{2}$

$\dpi{100} \frac{1}{2}\times \frac{1}{2}=\frac{1\times 1}{2\times 2}=\frac{1}{4}$ $\displaystyle \dpi{100} \frac{1}{2}\times \frac{1}{2}=\frac{1\times 1}{2\times 2}=\frac{1}{4}$

$\dpi{100} \frac{1}{4}$ $\displaystyle \dpi{100} \frac{1}{4}$ in decimal form is 0.25.

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Example Question #2 : Properties Of Exponents

$\dpi{100} (0.75)^{2}=$ $\displaystyle \dpi{100} (0.75)^{2}=$

Possible Answers:

$\dpi{100} 5.85$ $\displaystyle \dpi{100} 5.85$

$\dpi{100} 49.5$ $\displaystyle \dpi{100} 49.5$

$\dpi{100} \frac{9}{16}$ $\displaystyle \dpi{100} \frac{9}{16}$

$\dpi{100} 58.5$ $\displaystyle \dpi{100} 58.5$

Correct answer:

$\dpi{100} \frac{9}{16}$ $\displaystyle \dpi{100} \frac{9}{16}$

Explanation:

Convert .75 to a fraction. $\dpi{100} \frac{75}{100}=\frac{3}{4}$ $\displaystyle \dpi{100} \frac{75}{100}=\frac{3}{4}$.

Now multiply $\dpi{100} \frac{3}{4}\times \frac{3}{4}=\frac{3\times 3}{4\times 4}=\frac{9}{16}$ $\displaystyle \dpi{100} \frac{3}{4}\times \frac{3}{4}=\frac{3\times 3}{4\times 4}=\frac{9}{16}$

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Example Question #3 : Properties Of Exponents

$(-4)^{2} + (-4)^{3}$ $\displaystyle (-4)^{2} + (-4)^{3}$

Possible Answers:

$\displaystyle 80$

$\displaystyle -80$

-1,024 $\displaystyle -1,024$

$\displaystyle 48$

$\displaystyle -48$

Correct answer:

$\displaystyle -48$

Explanation:

$(-4)^{2} = -4 \cdot (-4) = +(4\cdot 4) = 16$ $\displaystyle (-4)^{2} = -4 \cdot (-4) = +(4\cdot 4) = 16$

$(-4)^{3} = -4 \cdot (-4)\cdot (-4) = 16 \cdot (-4) = - (16 \cdot 4) = -64$ $\displaystyle (-4)^{3} = -4 \cdot (-4)\cdot (-4) = 16 \cdot (-4) = - (16 \cdot 4) = -64$

Therefore,

$(-4)^{2} + (-4)^{3} = 16 + (-64) = - (64-16) = -48$ $\displaystyle (-4)^{2} + (-4)^{3} = 16 + (-64) = - (64-16) = -48$

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Example Question #2 : How To Find The Properties Of An Exponent

Express 0.00000000000097 in scientific notation.

Possible Answers:

$0.97 \times 10 ^{-13}$ $\displaystyle 0.97 \times 10 ^{-13}$

$9.7 \times 10 ^{-12}$ $\displaystyle 9.7 \times 10 ^{-12}$

$9.7 \times 10 ^{-13}$ $\displaystyle 9.7 \times 10 ^{-13}$

$0.97 \times 10 ^{-12}$ $\displaystyle 0.97 \times 10 ^{-12}$

$97 \times 10 ^{-14}$ $\displaystyle 97 \times 10 ^{-14}$

Correct answer:

$9.7 \times 10 ^{-13}$ $\displaystyle 9.7 \times 10 ^{-13}$

Explanation:

To rewrite a very small number in scientific notation:

Write the number.

$\displaystyle 0.00000000000097$

Move the decimal point right as many places as needed until it follows the first nonzero digit, which here is the nine. Count the number of places it is moved - here it will be thirteen places.

The number formed is 9.7 $\displaystyle 9.7$, which will be placed in front; $\displaystyle -13$, the negative of the number of places counted, will be the exponent. The number, in scientific notation, will be $9.7 \times 10 ^{-13}$ $\displaystyle 9.7 \times 10 ^{-13}$.

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Example Question #62 : Ssat Upper Level Quantitative (Math)

Evaluate:

$\frac{\left ( -5\right ) ^{5} - 5^{5}}{\left ( -5\right ) ^{5} + 5^{5}}$ $\displaystyle \frac{\left ( -5\right ) ^{5} - 5^{5}}{\left ( -5\right ) ^{5} + 5^{5}}$

Possible Answers:

$-\frac{2}{3,125}$ $\displaystyle -\frac{2}{3,125}$

-6,250 $\displaystyle -6,250$

$\displaystyle 0$

$-\frac{1}{6,250}$ $\displaystyle -\frac{1}{6,250}$

The quantity is undefined.

Correct answer:

The quantity is undefined.

Explanation:

$5^{5} = 5 \times 5 \times 5 \times 5 \times 5 = 3,125$ $\displaystyle 5^{5} = 5 \times 5 \times 5 \times 5 \times 5 = 3,125$

$\left (-5 \right ) ^{5} = -\left ( 5^{5} \right ) = -3,125$ $\displaystyle \left (-5 \right ) ^{5} = -\left ( 5^{5} \right ) = -3,125$

$\frac{\left ( -5\right ) ^{5} - 5^{5}}{\left ( -5\right ) ^{5} + 5^{5}} = \frac{-3,125 -3,125}{-3,125 + 3,125} =\frac{-6,250}{0}$ $\displaystyle \frac{\left ( -5\right ) ^{5} - 5^{5}}{\left ( -5\right ) ^{5} + 5^{5}} = \frac{-3,125 -3,125}{-3,125 + 3,125} =\frac{-6,250}{0}$

This is an undefined quantity.

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Example Question #11 : Generate Equivalent Numerical Expressions: Ccss.Math.Content.8.Ee.A.1

Evaluate:

$\frac{4^{4}}{4^{4} +\left ( -4 \right ) ^{4} }$ $\displaystyle \frac{4^{4}}{4^{4} +\left ( -4 \right ) ^{4} }$

Possible Answers:

$\displaystyle 0$

The quantity is undefined.

$\frac{1}{256}$ $\displaystyle \frac{1}{256}$

$\frac{1}{2}$ $\displaystyle \frac{1}{2}$

$-\frac{1}{2}$ $\displaystyle -\frac{1}{2}$

Correct answer:

$\frac{1}{2}$ $\displaystyle \frac{1}{2}$

Explanation:

$4^{4} = 4 \times 4 \times 4 \times 4 = 256$ $\displaystyle 4^{4} = 4 \times 4 \times 4 \times 4 = 256$

$\left (- 4 \right ) ^{4} = \left (- 4 \right ) \times \left (- 4 \right ) \times \left (- 4 \right ) \times \left (- 4 \right ) = 256$ $\displaystyle \left (- 4 \right ) ^{4} = \left (- 4 \right ) \times \left (- 4 \right ) \times \left (- 4 \right ) \times \left (- 4 \right ) = 256$

$\frac{4^{4}}{4^{4} +\left ( -4 \right ) ^{4} } = \frac{256 }{256 + 256} = \frac{256 }{512} =\frac{1 }{2}$ $\displaystyle \frac{4^{4}}{4^{4} +\left ( -4 \right ) ^{4} } = \frac{256 }{256 + 256} = \frac{256 }{512} =\frac{1 }{2}$

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Example Question #4 : How To Find The Properties Of An Exponent

Evaluate:

$(100 - 4 \cdot 25) ^{100 \div 25 }$ $\displaystyle (100 - 4 \cdot 25) ^{100 \div 25 }$

Possible Answers:

$\displaystyle 100,000,000$

$\displaystyle 0$

$\displaystyle 1$

100 $\displaystyle 100$

The expression is undefined.

Correct answer:

$\displaystyle 0$

Explanation:

$(100 - 4 \cdot 25) ^{100 \div 25 } = (100 - 100) ^{4} = 0 ^{4} =0$ $\displaystyle (100 - 4 \cdot 25) ^{100 \div 25 } = (100 - 100) ^{4} = 0 ^{4} =0$

as 0 taken to any positive power is equal to 0.

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SSAT Upper Level Math : How to find the properties of an exponent

Study concepts, example questions & explanations for SSAT Upper Level Math

All SSAT Upper Level Math Resources

Example Questions

Example Question #2 : Expressions & Equations

Example Question #2 : How To Find The Properties Of An Exponent

Example Question #1 : How To Find The Properties Of An Exponent

Example Question #1 : Properties Of Exponents

Example Question #2 : Properties Of Exponents

Example Question #3 : Properties Of Exponents

Example Question #2 : How To Find The Properties Of An Exponent

Example Question #62 : Ssat Upper Level Quantitative (Math)

Example Question #11 : Generate Equivalent Numerical Expressions: Ccss.Math.Content.8.Ee.A.1

Example Question #4 : How To Find The Properties Of An Exponent

All SSAT Upper Level Math Resources

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