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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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3 0
3 years ago
Solve each radical equation. Be sure to check your solutionsa)√(x+5)-9=-12b)√(4x-7)=√(3x+9)
Arlecino [84]

Answer:

a) There is no solution to the equation.

b) Solution: x = 16

Step-by-step explanation:

Hi there!

a) Let´s write the equation:

√(x + 5) - 9 = -12

add 9 to both sides of the equation

√(x + 5) = -12 + 9

√(x + 5) = -3

Square both sides of the equation

x + 5 = 9

Subtract 5 to both sides

x = 9 - 5

x = 4

Let´s check the solution:

√(x + 5) - 9 = -12

√(4 + 5) - 9 = -12

√9 - 9 = -12

3 - 9 = -12

-6 ≠ -12

Then x = 4 is not a solution to the equation.

b) Let´s write the equation:

√(4x - 7) = √(3x + 9)

square both sides of the equation  

4x - 7 = 3x + 9

subtract 3x and add 7 to both sides of the equation

4x - 3x = 9 + 7

x = 16

Let´s check the solution:

√(4x - 7) = √(3x + 9)

x = 16

√(4(16) - 7) = √(3(16) + 9)

√57 = √57

Then x = 16 is the solution to the equation

5 0
3 years ago
Which equation matches the graph?
aalyn [17]

Answer:

i think 4x+3y = -24 is answer

3 0
2 years ago
For two functions, m(x) and p(x), a statement is made that m(x) = p(x) at x = 7. What is definitely true about x = 7?
Shkiper50 [21]

For this case we have the following functions:

m (x)

p (x)

Where,

x: independent variable

m, p: dependent variables

For the value of x = 7 we have:

m (7)

p (7)

For this case it is true that:

m (7) = p (7)

Therefore, both functions have the same output argument for the same input value.

Answer:

C) Both m (x) and p (x) have the same output value at x = 7.

4 0
3 years ago
Read 2 more answers
Please help , and explain because i keep getting it wrong and it’s getting on my nerves
skad [1K]

Answer:

Olga's mistake: She did not multiply \frac{1}{4} and \frac{1}{3} in the beginning

Step-by-step explanation:

The main problem is that when a number is outside of the parentheses on the left side, then you have to multiply that number, in this case \frac{1}{4}, by both numbers in the parentheses. After that, continue solving the problem as you usually would. Hope this helped!

8 0
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