Exponents
Name _____________________________________________________ Date __________________
Score _________
Keywords: Exponents
Questions
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1.
Which operation is the opposite of multiplication?
20 points
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2.
In the expression, \( (14x^2) \) what is the coefficient?
20 points
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3.
In the expression, $ (x^3) $ what is the coefficient?
Hint: What hidden value must exist for this expression to equal more than zero?
20 points
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4.
Solve: \( (8m^2)(3m^3) \)
20 points
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5.
\( (-3a^2b^4)(-2b) \)
20 points
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6.
Solve: \( \dfrac{-24 a^{10} b^3}{5 a^3} \)
20 points
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7.
Solve: \( (-2xy^2)^6 \)
20 points
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8.
Simplify: \( 36^{\frac{{\color{red}1}}{{\color{teal}2}}} \)
20 points
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9.
Simplify: \( 144^{\frac{{\color{red}1}}{{\color{teal}2}}} \)
20 points
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10.
Simplify: \( 81^{\frac{{\color{red}3}}{{\color{teal}4}}} \)
20 points
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| Possible Points: 200 | |
Questions
|
1.
Which operation is the opposite of multiplication?
20 points
|
|
|
2.
In the expression, \( (14x^2) \) what is the coefficient?
20 points
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3.
In the expression, \( (x^3) \) what is the coefficient?
Hint: What hidden value must exist for this expression to equal more than zero?
20 points
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4.
Solve: ( (8m^2)(3m^3)$
20 points
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5.
\( (-3a^2b^4)(-2b)$
20 points
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6.
Solve: ( \dfrac{-24 a^{10} b^3}{5 a^3}$
20 points
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7.
Solve: ( (-2xy^2)^6$
20 points
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8.
Simplify: ( 36^{\frac{{\color{red}1}}{{\color{teal}2}}}$
20 points
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9.
Simplify: ( 144^{\frac{{\color{red}1}}{{\color{teal}2}}}$
20 points
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10.
Simplify: ( 81^{\frac{{\color{red}3}}{{\color{teal}4}}}$
20 points
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| Possible Points: 200 | |
Solutions
- Division
- The coefficient of $14x^2 \textit{ is } 14$.
- The coefficient of $ (x^3) $ is 1.
- \begin{align} (8m^2)(3m^3) &= (8 \times 3)(m^2m^3) \\ &= 24m^5 \end{align}
- \begin{align} (-3 a^2 b^4)(-2b) &= (-3 \times -2)(a^2 b^4 b^1) \\ &= 6 a^2 b^5 \end{align}
- \begin{align} \dfrac{-24 a^{10} b^3}{5 a^3} &= \left \( \dfrac{-25}{5} \right \) \left \( \dfrac{a^{10}}{a^3} \right \) \left \( \dfrac{b^3}{b^0} \right \) \\ &= -5 a^7 b^3 \end{align}
- \begin{align} (-2xy^2)^6 &= (-2^6)(x^6)(y^{2\times6}) \\ &= 64x^6y^{12} \end{align}
- \begin{align} 36^{\frac{{\color{red}1}}{{\color{teal}2}}} &= \sqrt[{\color{teal}2}]{36}^{{\color{red},1}} \\ &= \sqrt[{\color{teal}2}]{{\color{teal}(6)(6)}}^{{\color{red},1}} \\ &= 6^{{\color{red}1}} \\ &= 6 \end{align}
- \begin{align} 144^{\frac{{\color{red}1}}{{\color{teal}2}}} &= \sqrt[{\color{teal}2}]{144}^{{\color{red},1}} \\ &=\sqrt[{\color{teal}2}]{{\color{teal}(12)(12)}}^{{\color{red},1}} \\ &= 12^{{\color{red}1}} \\ &= 12 \end{align}
- \begin{align} 81^{\frac{{\color{red}3}}{{\color{teal}4}}} &= \sqrt[{\color{teal}4}]{81}^{{\color{red},3}} \\ &= \sqrt[{\color{teal}4}]{{\color{teal}(3)(3)(3)(3)}}^{{\color{red},3}} \\ &= 3^{{\color{red}3}} \\ &= 27 \end{align}
- Division
- The coefficient of \( (14x^2) \) is 14.
- The coefficient of \( (x^3) \) is 1.
- \begin{align} (8m^2)(3m^3) &= (8 \times 3)(m^2m^3) \\\ &= 24m^5 \end{align}
- \begin{align} (-3 a^2 b^4)(-2b) &= (-3 \times -2)(a^2 b^4 b^1) \\\ &= 6 a^2 b^5 \end{align}
- \begin{align} \dfrac{-24 a^{10} b^3}{5 a^3} &= \left \( \dfrac{-25}{5} \right \) \left \( \dfrac{a^{10}}{a^3} \right \) \left \( \dfrac{b^3}{b^0} \right \) \\\ &= -5 a^7 b^3 \end{align}
- \begin{align} (-2xy^2)^6 &= (-2^6)(x^6)(y^{2\times6}) \\\ &= 64x^6y^{12} \end{align}
- \begin{align} 36^{\frac{{\color{red}1}}{{\color{teal}2}}} &= \sqrt[{\color{teal}2}]{36}^{{\color{red},1}} \\\ &= \sqrt[{\color{teal}2}]{{\color{teal}(6)(6)}}^{{\color{red},1}} \\\ &= 6^{{\color{red}1}} \\\ &= 6 \end{align}
- \begin{align} 144^{\frac{{\color{red}1}}{{\color{teal}2}}} &= \sqrt[{\color{teal}2}]{144}^{{\color{red},1}} \\\ &=\sqrt[{\color{teal}2}]{{\color{teal}(12)(12)}}^{{\color{red},1}} \\\ &= 12^{{\color{red}1}} \\\ &= 12 \end{align}
- \begin{align} 81^{\frac{{\color{red}3}}{{\color{teal}4}}} &= \sqrt[{\color{teal}4}]{81}^{{\color{red},3}} \\\ &= \sqrt[{\color{teal}4}]{{\color{teal}(3)(3)(3)(3)}}^{{\color{red},3}} \\\ &= 3^{{\color{red}3}} \\\ &= 27 \end{align}