Find the number of permutations of the first 12 letters taken 3 at a time.

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

malfutka [58]

$\bf a^{\frac{{ n}}{{ m}}} \implies \sqrt[{ m}]{a^{ n}} \qquad \qquad
\sqrt[{ m}]{a^{ n}}\implies a^{\frac{{ n}}{{ m}}}
\\\\\\
\left.\qquad \qquad \right.\textit{negative exponents}\\\\
a^{-{ n}} \implies \cfrac{1}{a^{ n}}
\qquad \qquad
\cfrac{1}{a^{ n}}\implies a^{-{ n}}
\qquad \qquad 
a^{{{ n}}}\implies \cfrac{1}{a^{-{{ n}}}}\\\\
-------------------------------\\\\$

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

$\bf \cfrac{81^{\frac{1}{4}}x^{\frac{3}{4}}x^{-\frac{2}{4}}}{ y^{\frac{1}{4}}y^{\frac{1}{12}}}\implies \cfrac{(3^4)^{\frac{1}{4}}x^{\frac{3}{4}-\frac{2}{4}}}{y^{\frac{1}{4}+\frac{1}{12}}}\implies \cfrac{3^{4\cdot \frac{1}{4}}x^{\frac{1}{4}}}{y^{\frac{4}{12}}}\implies \cfrac{3^{\frac{4}{4}}x^{\frac{1}{4}}}{y^{\frac{1}{3}}}
\\\\\\
\cfrac{3\sqrt[4]{x}}{\sqrt[3]{y}}$

7 0

2 years ago

(Apex 2.2.4 math 8)

Gennadij [26K]

Answer: D

Step-by-step explanation: slope = "rise over run" = 1.5/18 = 3/36 = 1/12 for the 1st section to the landing

slope is the change in height, the vertical change, divided by the change in horizontal distance

2nd section has slope 1/18 and covers 9 feet. That means it rises 1/2 foot

slope = 1/18 = (1/2)/9

the door is 2 feet higher than the ground level, 1.5 + .5 = 2 feet change vertically

5 0

2 years ago

Read 2 more answers

Given f (x) = 1/4x-3/4<br> Find f^-1

Snowcat [4.5K]

The inverse of a function f(x) is f⁻¹(x) = 4x + 3 after using the concept of the inverse of a function.

<h3>What is a function?</h3>

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

We have a function:

$\rm f(x) = \dfrac{1}{4}x-\dfrac{3}{4}$