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2 years ago

Simplify (x^2)^35x/6x^215x^3

Mathematics

1 answer:

nasty-shy [4]2 years ago

8 0

When we Simplify [(x^2)^3 × 5x] / [6x^2 × 15x^3], the result obtained is (1/18)x^2

<h3>Data obtained from the question</h3>

[(x^2)^3 × 5x] / [6x^2 × 15x^3]
Simplification =?

<h3>How to simplify [(x^2)^3 × 5x] / [6x^2 × 15x^3]</h3>

[(x^2)^3 × 5x] / [6x^2 × 15x^3]

Recall

(M^a)^b = M^ab

Thus,

(x^2)^3 = x^6

[(x^2)^3 × 5x] / [6x^2 × 15x^3] = [x^6 × 5x] / [6x^2 × 15x^3]

Recall

M^a × M^b = M^(a+b)

Thus,

x^6 × 5x = 5x^(6 + 1) = 5x^7

6x^2 × 15x^3] = (6×15)x^(2 + 3) = 90x^5

[x^6 × 5x] / [6x^2 × 15x^3] = 5x^7 / 90x^5

Recall

M^a ÷ M^b = M^(a - b)

Thus,

5x^7 ÷ 90x^5 = (5÷90)x^(7 - 5) = (1/18)x^2

Therefore,

[(x^2)^3 × 5x] / [6x^2 × 15x^3] = (1/18)x^2

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Step-by-step explanation:

$\textsf{\large{\underline{Solution}:}}$

<h3><u>Given That:</u></h3>

$\rm: \longmapsto (3 - 4i)(x + iy) = 1 + 0i$

$\rm: \longmapsto 3(x + iy) - 4i(x + iy)= 1 + 0i$

$\rm: \longmapsto 3x + 3iy - 4ix +4y= 1 + 0i$

<u>On rearranging the terms, we get:</u>

$\rm: \longmapsto (3x + 4y)+ (3y - 4x)i = 1 + 0i$

<u>Comparing both sides, we get:</u>

$\rm: \longmapsto 3x + 4y = 1 --- (i)$

$\rm: \longmapsto 3y - 4x = 0 --- (ii)$

<u>Multiplying (i) by 4, we get:</u>

$\rm: \longmapsto 12x + 16y = 4--- (iii)$

<u>Multiplying (ii) by 3, we get:</u>

$\rm: \longmapsto 9y - 12x = 0 --- (iv)$

<u>Adding equations (iii) and (iv), we get:</u>

$\rm: \longmapsto25y = 4$

$\rm: \longmapsto y =\dfrac{4}{25}$

<u>From (ii), we get:</u>

$\rm: \longmapsto 3y - 4x = 0$

$\rm: \longmapsto 3y = 4x$

$\rm: \longmapsto x = \dfrac{3}{4} y$

$\rm: \longmapsto x = \dfrac{3}{4} \times \dfrac{4}{25}$

$\rm: \longmapsto x = \dfrac{3}{25}$

<u>Therefore:</u>

$\rm: \longmapsto (x,y)= \bigg( \dfrac{3}{25}, \dfrac{4}{25} \bigg)$

★ <u>Which is our required answer.</u>

$\textsf{\large{\underline{More To Know}:}}$

$\rm1.\ i^{4n} = 1$

$\rm2. \ i^{4n+1} = i$

$\rm3.\ i^{4n+2} = -1$

$\rm4.\ i^{4n+3} = -i$

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3 years ago

Simplify (x^2)^3*5x/6x^2*15x^3

Simplify (x^2)^35x/6x^215x^3