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GalinKa [24]
3 years ago
14

Simplify the expression to one number using order of operations:

Mathematics
1 answer:
geniusboy [140]3 years ago
5 0
<h2><u>COMBINED OPERATIONS</u></h2><h3>Exercise</h3>

First, let's solve the subtraction (in parentheses):

\mathsf{\dfrac{-8\left(2-6\right)}{2}}

\mathsf{\dfrac{-8(-4)}{2}}

Now, let's solve the multiplication. Remember: in multiplication, two negative numbers will give a positive number:

\mathsf{\dfrac{-8(-4)}{2}}

\mathsf{\dfrac{32}{2}}

Finally, let's solve the division:

\mathsf{\dfrac{32}{2} = 16}

<h3><u>Answer</u>: 16</h3>
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<img src="https://tex.z-dn.net/?f=%20%7B2%7D%5E%7Bm%7D%20%20%3D%20n%20" id="TexFormula1" title=" {2}^{m} = n " alt=" {2}^{m} =
sveta [45]

Answer:

\displaystyle n^3-\frac{1}{n^{2}}

Step-by-step explanation:

<u>Exponents Properties</u>

We need to recall the following properties of exponents:

(a^x)^y=(a^y)^x=a^{xy}

\displaystyle a^{-x}=\frac{1}{a^x}

We are given the expression:

2^m=n

We need to express the following expression in terms of n.

8^m-4^{-m}

It's necessary to modify the expression to use the given equivalence.

Recall 8=2^3 \text{ and }4 = 2^2. Thus:

(2^3)^m-(2^2)^{-m}

Applying the property:

(2^m)^3-(2^m)^{-2}

Substituting the given expression:

n^3-n^{-2}

Or, equivalently:

\mathbf{\displaystyle 8^m-4^{-m}= n^3-\frac{1}{n^{2}}}

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3 years ago
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Step-by-step explanation:

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