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german
3 years ago
12

What is the simplified expression for,

Mathematics
1 answer:
Nostrana [21]3 years ago
6 0

Here are a few rules you need to know for this equation:

  • Multiplying exponents of the same base: x^m\times x^n=x^{m+n}
  • Dividing exponents of the same base: \frac{x^m}{x^n}=x^{m-n}
  • Turning a negative exponent to a positive one: x^{-m}=\frac{1}{x^m};\frac{1}{x^{-m}}=x^m

So this is our algebraic expression: \frac{3^{-4}\times 2^3\times 3^2}{2^4\times 3^{-3}}

Firstly, multiply 3^-4 and 3^2: \frac{3^{-4+2}\times 2^3}{2^4\times 3^{-3}}=\frac{3^{-2}\times 2^3}{2^4\times 3^{-3}}

Next, divide:

\frac{3^{-2}\times 2^3}{2^4\times 3^{-3}}=3^{-2-(-3)}2^{3-4}=3^12^{-1}

Next, turn the negative exponent into a positive one: 3^12^{-1}= \frac{3}{2}

<u>Your final answer is 3/2, or 1.5.</u>

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Given:

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Divide the data set in two equal parts.

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Divide each parenthesis in two equal parts.

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Now,

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The interquartile range is:

IQR=Q_3-Q_1

IQR=16-12

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The data values lies outside the interval [Q_1-1.5IQR,Q_3+1.5IQR] are known as outliers.

[Q_1-1.5IQR,Q_3+1.5IQR]=[12-1.5(4),16+1.5(4)]

[Q_1-1.5IQR,Q_3+1.5IQR]=[12-6,16+6]

[Q_1-1.5IQR,Q_3+1.5IQR]=[6,22]

All the data values lie in the interval [6,22]. So, there are no outliers.

Hence, the correct option is 4.

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