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igor_vitrenko [27]
3 years ago
14

Simplify. Your answer should contain only positive exponents with no fractional exponents in the denominator.

Mathematics
1 answer:
mart [117]3 years ago
5 0

Answer:

\dfrac{x^{\frac{2}{3}}y^{\frac{1}{4}}}{4y^{2}}.

Step-by-step explanation:

The given expression is  

\dfrac{3y^{\frac{1}{4}}}{4x^{-\frac{2}{3}}y^{\frac{3}{2}}\cdot 3y^{\frac{1}{2}}}

We need to simplify the expression such that answer should contain only positive exponents with no fractional exponents in the denominator.

Using properties of exponents, we get

\dfrac{3}{4\cdot 3}\cdot \dfrac{y^{\frac{1}{4}}}{x^{-\frac{2}{3}}y^{\frac{3}{2}+\frac{1}{2}}}    [\because a^ma^n=a^{m+n}]

\dfrac{1}{4}\cdot \dfrac{y^{\frac{1}{4}}}{x^{-\frac{2}{3}}y^{2}}

\dfrac{1}{4}\cdot \dfrac{x^{\frac{2}{3}}y^{\frac{1}{4}}}{y^{2}}         [\because a^{-n}=\dfrac{1}{a^n}]

\dfrac{x^{\frac{2}{3}}y^{\frac{1}{4}}}{4y^{2}}

We can not simplify further because on further simplification we get negative exponents in numerator or fractional exponents in the denominator.

Therefore, the required expression is \dfrac{x^{\frac{2}{3}}y^{\frac{1}{4}}}{4y^{2}}.

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Which best explains why 5 x 4 is greater than 5 x 1/4 ?
zmey [24]
Because one is put into fraction form. Therefore the one in fraction form is going to be smaller. 5*4=20 and 5*1/4=1.25. I hope my answer helped you.
3 0
3 years ago
jeffery plans to rent a beach house for his sister's birthday and will use his savings pay for it. The company charges a $25.00
finlep [7]

Answer:

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Step-by-step explanation:

The charge will be $25 + ($10/h)(6 h) = $25 +60 = $85.

Jeffrey's savings will decrease by $85, so the net change is -$85.

7 0
3 years ago
A cylindrical water tower has a height of 6 ft and a radius of 4 ft. How much water does the tower contain when it is 1/3 full?
viktelen [127]
V = pi r^2 h
But it says 1/3 full so
1/3 pi r^2 h
1/3 * 3.14 * 4^2 * 6
100.48ft cubed
Whichrounds off to 100.5
4 0
3 years ago
Who knows what 5 to the power of 2 i
Alexxandr [17]
If you mean 5^2 and not 5^2i then
5^2 just means 5 times itself,twice or 5 times 5 or 25


if you meant 5^2i
i=√-1
so law of exponents says a^(xz)=(a^x)^z so
5^2i=(5^2)^i or (25)^i
the answer (if you wanted 5^2i) is 25^i


IF YOU MEANT 5^2 then the answer is 25
6 0
3 years ago
Read 2 more answers
Graph each equation using the slope and y-intercept, y=-4x-2.5
VLD [36.1K]

Answer:

Slope:-4

y-int: -2.5

Step-by-step explanation:

x     y

0.   -2.5

1.    -6.5

6 0
3 years ago
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