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charle [14.2K]
3 years ago
15

((81x^3 y^(-1/3))^1/4)/(x^2 y)^1/4 simplify

Mathematics
1 answer:
malfutka [58]3 years ago
7 0
\bf a^{\frac{{ n}}{{ m}}} \implies  \sqrt[{ m}]{a^{ n}} \qquad \qquad
\sqrt[{ m}]{a^{ n}}\implies a^{\frac{{ n}}{{ m}}}
\\\\\\
\left.\qquad \qquad \right.\textit{negative exponents}\\\\
a^{-{ n}} \implies \cfrac{1}{a^{ n}}
\qquad \qquad
\cfrac{1}{a^{ n}}\implies a^{-{ n}}
\qquad \qquad 
a^{{{  n}}}\implies \cfrac{1}{a^{-{{  n}}}}\\\\
-------------------------------\\\\

\bf \cfrac{\left( 81x^3y^{-\frac{1}{3}} \right)^{\frac{1}{4}}}{(x^2y)^{\frac{1}{4}}}\implies \cfrac{81^{\frac{1}{4}}x^{3\cdot {\frac{1}{4}}}y^{-\frac{1}{3}\cdot {\frac{1}{4}}}}{x^{2\cdot {\frac{1}{4}}}y^{\frac{1}{4}}}\implies
\cfrac{81^{\frac{1}{4}}x^{\frac{3}{4}}y^{-\frac{1}{12}}}{x^{\frac{2}{4}} y^{\frac{1}{4}}}

\bf \cfrac{81^{\frac{1}{4}}x^{\frac{3}{4}}x^{-\frac{2}{4}}}{ y^{\frac{1}{4}}y^{\frac{1}{12}}}\implies \cfrac{(3^4)^{\frac{1}{4}}x^{\frac{3}{4}-\frac{2}{4}}}{y^{\frac{1}{4}+\frac{1}{12}}}\implies \cfrac{3^{4\cdot \frac{1}{4}}x^{\frac{1}{4}}}{y^{\frac{4}{12}}}\implies \cfrac{3^{\frac{4}{4}}x^{\frac{1}{4}}}{y^{\frac{1}{3}}}
\\\\\\
\cfrac{3\sqrt[4]{x}}{\sqrt[3]{y}}
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The rectangle below has an area of 1 8 x 3 18x 3 square meters and a length of 2 x 2 2x 2 meters.
motikmotik

Answer:

\text{The width of rectangle}=9x\text{ meters}

Step-by-step explanation:

We have been given that the rectangle has an area of 18x^3 square meters and a length of 2x^{2}. We are asked to find the width of rectangle.

Since we know that area of a rectangle is width times length of the rectangle, so we can find width of our given rectangle by dividing given area by length of rectangle.

\text{Area of rectangle}=\text{Width of rectangle *Length of the rectangle}

\frac{\text{Area of rectangle}}{\text{Length of rectangle}}=\frac{\text{Width of rectangle *Length of the rectangle}}{\text{Legth of rectangle}}

\text{The width of rectangle}=\frac{\text{Area of rectangle}}{\text{Length of rectangle}}

Upon substituting our given values in above formula we will get,

\text{The width of rectangle}=\frac{18x^3\text{ meter}^2}{2x^2\text{ meters}}

\text{The width of rectangle}=\frac{9x^3\text{ meters}}{x^2}

Using exponent rule for quotient \frac{a^m}{a^n}=a^{m-n} we will get,

\text{The width of rectangle}=9x^{3-2}\text{ meters}

\text{The width of rectangle}=9x^{1}\text{ meters}=9x\text{ meters}

Therefore, width of our given rectangle will be 9x meters.

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Step-by-step explanation:

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Answer:

c) (-2, 1)

Step-by-step explanation:

3x - 3y = -9

2x + y = -3

2x + y = -3

-2x       -2x

y = -2x - 3

3x - 3y = -9

y = -2x - 3

3x - 3(-2x - 3) = -9

3x + 6x + 9 = -9

9x + 9 = -9

    - 9    -9

9x = -18

/9     /9

x = -2

y = -2x - 3

y = -2(-2) -3

y = 4 - 3

y = 1

(x, y) --> (-2,1)

Check your answer:

y = -2x - 3

1 = -2(-2) - 3

1 = 4 - 3

1 = 1

This statement is true

Hope this helps!

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