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2 years ago

Simplify 6/6^1/4 rational exponents

Mathematics

1 answer:

White raven [17]2 years ago

7 0

Answer:

we conclude that:

$\frac{6}{6^{\frac{1}{4}}}=6^{\frac{3}{4}}$

Step-by-step explanation:

Given

The expression is

$\frac{6}{6^{\frac{1}{4}}}$

To determine

Simplify the expression

Simplifying the expression

$\frac{6}{6^{\frac{1}{4}}}$

Apply the exponent rule: $\frac{x^a}{x^b}=x^{a-b}$

$\frac{6}{6^{\frac{1}{4}}}=6^{1-\frac{1}{4}}$

Subtract the numbers: $1-\frac{1}{4}=\frac{3}{4}$

$=6^{\frac{3}{4}}$

Therefore, we conclude that:

$\frac{6}{6^{\frac{1}{4}}}=6^{\frac{3}{4}}$

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Find thd <img src="https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7Bdx%7D" id="TexFormula1" title="\frac{dy}{dx}" alt="\frac{dy}{dx}" a

NARA [144]

$x^3y^2+\sin(x\ln y)+e^{xy}=0$

Differentiate both sides, treating $y$ as a function of $x$ . Let's take it one term at a time.

Power, product and chain rules:

$\dfrac{\mathrm d(x^3y^2)}{\mathrm dx}=\dfrac{\mathrm d(x^3)}{\mathrm dx}y^2+x^3\dfrac{\mathrm d(y^2)}{\mathrm dx}$

$=3x^2y^2+x^3(2y)\dfrac{\mathrm dy}{\mathrm dx}$

$=3x^2y^2+6x^3y\dfrac{\mathrm dy}{\mathrm dx}$

Product and chain rules:

$\dfrac{\mathrm d(\sin(x\ln y)}{\mathrm dx}=\cos(x\ln y)\dfrac{\mathrm d(x\ln y)}{\mathrm dx}$

$=\cos(x\ln y)\left(\dfrac{\mathrm d(x)}{\mathrm dx}\ln y+x\dfrac{\mathrm d(\ln y)}{\mathrm dx}\right)$

$=\cos(x\ln y)\left(\ln y+\dfrac1y\dfrac{\mathrm dy}{\mathrm dx}\right)$

$=\cos(x\ln y)\ln y+\dfrac{\cos(x\ln y)}y\dfrac{\mathrm dy}{\mathrm dx}$

Product and chain rules:

$\dfrac{\mathrm d(e^{xy})}{\mathrm dx}=e^{xy}\dfrac{\mathrm d(xy)}{\mathrm dx}$

$=e^{xy}\left(\dfrac{\mathrm d(x)}{\mathrm dx}y+x\dfrac{\mathrm d(y)}{\mathrm dx}\right)$

$=e^{xy}\left(y+x\dfrac{\mathrm dy}{\mathrm dx}\right)$

$=ye^{xy}+xe^{xy}\dfrac{\mathrm dy}{\mathrm dx}$

The derivative of 0 is, of course, 0. So we have, upon differentiating everything,

$3x^2y^2+6x^3y\dfrac{\mathrm dy}{\mathrm dx}+\cos(x\ln y)\ln y+\dfrac{\cos(x\ln y)}y\dfrac{\mathrm dy}{\mathrm dx}+ye^{xy}+xe^{xy}\dfrac{\mathrm dy}{\mathrm dx}=0$

Isolate the derivative, and solve for it:

$\left(6x^3y+\dfrac{\cos(x\ln y)}y+xe^{xy}\right)\dfrac{\mathrm dy}{\mathrm dx}=-\left(3x^2y^2+\cos(x\ln y)\ln y-ye^{xy}\right)$

$\dfrac{\mathrm dy}{\mathrm dx}=-\dfrac{3x^2y^2+\cos(x\ln y)\ln y-ye^{xy}}{6x^3y+\frac{\cos(x\ln y)}y+xe^{xy}}$

(See comment below; all the 6s should be 2s)

We can simplify this a bit by multiplying the numerator and denominator by $y$ to get rid of that fraction in the denominator.

$\dfrac{\mathrm dy}{\mathrm dx}=-\dfrac{3x^2y^3+y\cos(x\ln y)\ln y-y^2e^{xy}}{6x^3y^2+\cos(x\ln y)+xye^{xy}}$

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2 years ago

The question is attached please help

Maksim231197 [3]

Answer:

area = 102 ft²

Step-by-step explanation:

(8x6) + (9x6) = 48 + 54 = 102 ft²

7 0

2 years ago

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omeli [17]

Answer:

mean= sum of the terms/ (over) number of terms

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2 years ago

The diameter of a circle is 222 units.<br> What is the radius of the circle?<br> units

cricket20 [7]

Answer:

111

Step-by-step explanation:

divide by 2 to find the radius

5 0

1 year ago

<img src="https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B9%7D" id="TexFormula1" title="\frac{1}{9}" alt="\frac{1}{9}" align="absmiddle

Jobisdone [24]

$\dfrac{1}{9} - \dfrac{5}{6}$

Set up

$\dfrac{2}{18} - \dfrac{15}{18}$

Get all fractions to a common denominator which will allow you to subtract them

$\dfrac{2 - 15}{18}$

Subtract numerators

$\boxed{- \dfrac{13}{18}}$

Simplify

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2 years ago