About Exponents & The Order of Operations:
Natural Number exponents give us a way to write a repeated multiplication of the same number in a more compact fashion. For example, we can write 6 factors of the number 8 as: 86. Additionally, we consider what happens when an exponential expression has a negative base. We need to consider the fact that -22 is not the same as (-2)2. The negative is only raised to the power if and only if it is enclosed inside of a set of parentheses. Lastly, we think about the order of operations or the order in which we perform operations when multiple operations are present. Generally, we remember this using the PEMDAS acronym, which stands for Parentheses, Exponents, Multiply/Divide (Left to Right), Add/Subtract (Left to Right).
Test Objectives
- Demonstrate the ability to identify the base and exponent in an exponential expression
- Demonstrate the ability to evaluate a number in exponential form
- Demonstrate the ability to simplify an exponential expression with a negative base
- Demonstrate the ability to simplify an expression using the steps in PEMDAS
#1:
Instructions: Identify the base and exponent
$$a)\hspace{.1em}5^4$$
$$b)\hspace{.1em}{-}3^6$$
$$c)\hspace{.1em}(-2)^5$$
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#2:
Instructions: Evaluate
$$a)\hspace{.1em}(-3)^3$$
$$b)\hspace{.1em}(-2)^6$$
$$b)\hspace{.1em}{-}5^4$$
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#3:
Instructions: Evaluate
$$a)\hspace{.1em}{-}3 \cdot 5^{2}- |2^{2}- 7 \cdot (-2)|$$
$$b)\hspace{.1em}\frac{15 \hspace{.1em} ÷ \hspace{.1em} ((-3) \cdot 2) + \frac{3}{2}}{|6 \cdot (-4)| ÷ (-12)}$$
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#4:
Instructions: Evaluate
$$a)\hspace{.1em}\frac{5^2 - 7 \cdot 14 + 4^3 \hspace{.1em} ÷ \hspace{.1em} 2}{|6 - 9^2| - 3\sqrt{16}+ 19}$$
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#5:
Instructions: Evaluate
$$a)\hspace{.1em}\frac{(-3^2 + 4) \cdot -2^2}{|3^4 - 5^3| \hspace{.1em} ÷ \hspace{.1em} (2^3 \cdot 11)}$$
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Written Solutions:
#1:
Solutions:
a) 5 » base, 4 » exponent
b) 3 » base, 6 » exponent (note: the negative is not part of the base)
b) -2 » base, 5 » exponent (note: the negative is part of the base)
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#2:
Solutions:
a) -27
b) 64
c) -625
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#3:
Solutions:
$$a)\hspace{.1em}{-93}$$
$$b)\hspace{.1em}\frac{1}{2}$$
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#4:
Solutions:
$$a)\hspace{.1em}{-}\frac{1}{2}$$
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#5:
Solutions:
a) 40
