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Mandarinka [93]
4 years ago
8

Simplify the expression (StartFraction 1 Over 4 a b EndFraction) Superscript negative 2. Assume a not-equals 0, b not-equals 0.

Mathematics
2 answers:
pashok25 [27]4 years ago
7 0

Answer:

The simplest form of the expression is 16 a²b²

Step-by-step explanation:

* <em>Lets explain how to solve the problem</em>

- To simplify any fraction with exponent you must put it with positive

 exponent

- Ex: the fraction (\frac{2}{3})^{-1} not in the simplest form

 because it has negative exponent

- To change the negative exponent to positive exponent reciprocal the

 fraction, (\frac{3}{2})^{1} and this is the simplest form of the fraction

* <em>Now lets solve the problem</em>

∵ The expression is (\frac{1}{4ab})^{-2}, where a and b ≠ 0

- At first reciprocal the fraction

∴ (\frac{1}{4ab})^{-2}=(\frac{4ab}{1})^{2}

- Then solve the power

∵ 4² = 16

∵ (ab)² = a²b²

∴ (4ab)² = 16 a²b²

* The simplest form of the expression is 16 a²b²

andrey2020 [161]4 years ago
4 0

Answer:

16 a²b² is option D on e2020

Step-by-step explanation:

100% on test

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If b is the midpoint of ac, ac=cd, ab=3x+4, ac=11x-17, and ce=49, find de
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First, we draw our line.

 

|------------------------------------------------------------------------------------|

a                                                                                                            e

 

 

Next, break up this line into segments using the information.

 

|----------------------|----------------------|--------------------|------------------|

a                            b                            c                         d                      e

 

 

The entire line is 29.

 

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ab + bc + cd + de = 29

 

You also know that

 

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Due to midpoint theorem,

 

ab = bc

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Then,

 

2ab + 2cd = 29

 

 

The equations we will use are

 

bd = bc + cd                       eq1

2bc + 2cd = 29                   eq2

 

 

Dividing both sides of the equation in eq2 yields

 

bc + cd = 14.5

 

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