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xxTIMURxx [149]
3 years ago
13

What is the simplified expression for 3 to the power of negative 4 multiplied by 2 to the power of 3 multiplied by 3 to the powe

r of 2 whole over 2 to the power of 4 multiplied by 3 to the power of negative 3?
A. 3 over 2
B. 3 to the power of 2 over 2 to the power of 2
C. 3 to the power of 2 over 2
D. 2 to the power of 4 over 3

Can somebody explain how to do this?

Mathematics
1 answer:
vlabodo [156]3 years ago
3 0
Ok first look at just the base 2s. 2^3/2^4 is 1/2
Then 3^-4*3^2/3^-3 is 3^-2/3^-3 is 3^3/3^2 is 3
Therefore the answer is 3/2
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What is the 10th term of the geometric sequence 400, 200, 100...?
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ANSWER

a_ {10} = \frac{25}{32}

EXPLANATION

The given geometric sequence is

400, 200, 100...

The first term is

a_1=400

The common ratio is

r =  \frac{200}{400}  =  \frac{1}{2}

The nth term is

a_n=a_1( {r}^{n - 1} )

We substitute the known values to get;

a_n=400(  \frac{1}{2} )^{n - 1}

a_ {10} =400(  \frac{1}{2} )^{10 - 1}

a_ {10} =400(  \frac{1}{2} )^{9}

a_ {10} = \frac{25}{32}

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