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ankoles [38]
3 years ago
14

Which expression is equivalent to The equation

Mathematics
2 answers:
Lostsunrise [7]3 years ago
3 0

Answer: last option.

Step-by-step explanation:

 The negative exponent rules establishes the following:

a^{-n}=\frac{1}{a^n}

The power to power property establishes:

(a^b)^c=a^{bc}

The product of powers property establishes that when you multiply two powers with equal base you must add the exponents.

Applying the properties, you obtain the equivalent expression shown below:

(\frac{1}{x^2*x^6})^3=(\frac{1}{x^8})^3=\frac{1}{x^{24}}

Therefore the answer is the last option.

Nitella [24]3 years ago
3 0

Answer:

The correct answer is last option 1/x²⁴

Step-by-step explanation:

Points to remember

1).  (x)⁻ᵃ = 1/xᵃ

2).  (xᵃ)ᵇ = xᵃᵇ

3).  xᵃ/xᵇ = xᵃ⁻ᵇ

It is given that, { x⁻⁶/x² }³

<u>To find the equivalent expression</u>

{ x⁻⁶/x² }³ = (x⁻⁶ ⁻ ²)³

 = (x⁻⁸)³

 = x⁻²⁴

 = 1/x²⁴

Therefore the correct answer is last option

{ x⁻⁶/x² }³  = 1/x²⁴

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What does i^739 equal? explain how you found your answer.
Sophie [7]
<h3>Answer:   -i</h3>

========================================================

Explanation:

i = sqrt(-1)

Lets list out the first few powers of i

  • i^0 = 1
  • i^1 = i
  • i^2 = -1
  • i^3 = i*i^2 = i*(-1) = -i
  • i^4 = (i^2)^2 = (-1)^2 = 1

By the time we reach the fourth power, we repeat the cycle over again (since i^0 is also equal to 1). The cycle is of length 4, which means we'll divide the exponent over 4 to find the remainder. Ignore the quotient. That remainder will determine if we go for i^0, i^1, i^2 or i^3.

For example, i^5 = i^1 because 5/4 leads to a remainder 1.

Another example: i^6 = i^2 since 6/4 = 1 remainder 2

Again, we only care about the remainder to find out which bin we land on.

-------------

Turning to the question your teacher gave you, we have,

739/4 = 184 remainder 3

So i^739 = i^3 = -i

<h3>-i is the final answer</h3>

--------------

Side notes:

  • if i^a = i^b, then a-b is a multiple of 4
  • Recall that the divisibility by 4 trick involves looking at the last two digits of the number. So i^739 is identical to i^39.
4 0
3 years ago
When you divide a whole number by fraction with a numerator of one explain how you can find the quotient
MariettaO [177]
In this item, we are asked for the methodology to arriving the answer when the whole number is divided by a fraction with 1 as a numerator. If example we have the whole number as 4 and the fraction with 1 as numerator is 1/2, the division would become, 4/(1/2). We multiply the whole number by the reciprocal of the given fraction which then becomes, 4(2/1). The final answer would be 12.

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6 0
4 years ago
Mateo reproducira una foto que mide 5 cm por lado a una escala de 3/4
Aneli [31]

the question in English

Mateo will reproduce a photo measuring 5 cm per side on a scale of 3/4

How much will the square side of the copy measure?

Will the size of the copy be larger or smaller than the original?

we know that

the scale factor is equal to \frac{3}{4}

Let

x----------> the original length side

y--------> the copy length side

y=\frac{3}{4}*x

we have that

x=5\ cm

substitute the values

y=\frac{3}{4}*5=3.75\ cm

therefore

<u>the answer Part a) is </u>

the length side of the copy measure is 3.75\ cm

Part b)

we know that

the size of the original photo is------> 5*5=25\ cm^{2}

the size of the copy is------> 3.75*3.75=14.06\ cm^{2}

so

14.06\ cm^{2} < 25\ cm^{2}

therefore

<u>the answer part b) is</u>

The size of the copy be smaller than the original



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