All categories

2 years ago

Simplify the expression.

Mathematics

2 answers:

alexira [117]2 years ago

3 0

we have

$\sqrt[4]{768x^{8}y^{5}}$

we know that

$\sqrt[4]{768x^{8}y^{5}}=({768x^{8}y^{5})^{\frac{1}{4}}$

$768=2^{8} *3$

$({768x^{8}y^{5})^{\frac{1}{4}}=({2^{8}3x^{8}y^{5})^{\frac{1}{4}}$

$({2^{8}3x^{8}y^{5})^{\frac{1}{4}}=2^{2} x^{2}y (3y)^{\frac{1}{4}}=4x^{2}y\sqrt[4]{3y}$

therefore

the answer is the option C

$4x^{2}y\sqrt[4]{3y}$

lutik1710 [3]2 years ago

3 0

Answer

Explanation

⁴√(768x⁸y⁵) = (768x⁸y⁵)¹/⁴

=768¹/⁴ × x⁸ˣ¹/⁴ × y⁵ˣ¹/⁴

⁴√768 = ⁴√(3 × 256)

= 4 ⁴√3

x⁸ˣ¹/⁴ = x²

y⁵ˣ¹/⁴ = (y⁴ × y¹)¹/⁴

= y⁴ˣ¹/⁴ × y¹/⁴

= y × y¹/⁴

∴⁴√(768x⁸y⁵) = (768x⁸y⁵)¹/⁴

= 4x²y ⁴√(3y)

The answer is C.

You might be interested in

Insert <, >, or = to make the sentence true. √3 √7

Black_prince [1.1K]

< is going to be your answer

4 0

2 years ago

Read 2 more answers

If the battery costs $75 and has a life of 300 charge-discharge cycles, what is the cost of the energy in dollars per kilowatt h

kumpel [21]

Answer:

I'm sorry but no idea

Step-by-step explanation:

No idea

3 0

2 years ago

How to answer this question??? thanks

vesna_86 [32]

$\dfrac{2m}{5}+3=7(4m-3)\ \ \ \ |use\ distributive\ property:a(b-c)=ab-ac\\\\\dfrac{2m}{5}+3=28m-21\ \ \ \ \ |multiply\ both\ sides\ by\ 5\\\\2m+15=140m-105\ \ \ \ |subtract\ 140m\ from\ both\ sides\\\\-138m+15=-105\ \ \ \ |subtract\ 15\ from\ both\ sides\\\\-138m=-120\ \ \ \ |divide\ both\ sides\ by\ (-138)\\\\m=\dfrac{120:6}{138:6}\\\\\boxed{m=\frac{20}{23}}$

7 0

2 years ago

Find the length of the curve y = 3/5x^5/3 - 3/4x^1/3 + 6 for 1 < = x < = 8. The length of the curve is . (Type an exact an

Mashutka [201]

Answer:

$\sqrt\frac{387}{20}$

Step-by-step explanation:

$Arc Length =\int\limits^a_b {\sqrt{1+(\frac{dy}{dx})^2 } } \, dx$

$y=\dfrac{3}{5}x^{\frac{5}{3}}- \dfrac{3}{4}x^{\frac{1}{3}}+6$

$\frac{dy}{dx} =x^{\frac{2}{3}}-\dfrac{1}{4}x^{-\frac{2}{3}}$

$1+(\frac{dy}{dx})^2 }=1+(x^{\frac{2}{3}}-\dfrac{1}{4}x^{-\frac{2}{3}})^2\\=1+(x^{\frac{4}{3}}-\dfrac{1}{2}+ \dfrac{1}{16}x^{-\frac{4}{3}})$

$=\dfrac{1}{2}+x^{\frac{4}{3}}+ \dfrac{1}{16}x^{-\frac{4}{3}}$

For the Interval $1\leq x\leq 8$

Length of the Curve $=\int\limits^8_1 {\sqrt{\dfrac{1}{2}+x^{\frac{4}{3}}+ \dfrac{1}{16}x^{-\frac{4}{3}} } } \, dx\\$

Using T1-Calculator

$=\sqrt\frac{387}{20}$

3 0

2 years ago

A chemical factory has 2 cylindrical chemical tanks, one containing Chemical X and the other containing Chemical Y. The tank con

Mashutka [201]

The tank with Chemical X "takes up" a space of 25ft³. Ordinarily we think of something "taking up" space as being area or surface area; however, area is a square measurement, and this is cubic; this must be volume. The volume of the tank with Chemical X is 1.5 times the volume of the tank containing Chemical Y; setting this up in an equation we would have
25 = 1.5V
We would divide both sides by 1.5 to get the volume of the tank containing Chemical Y:
$\frac{25}{1.5}=\frac{1.5V}{1.5} \\16 \frac{2}{3}=V$
To find the volume of a cylinder, we find the base area and multiply by the height. We know the volume and we know the base area, so our equation to find the height of the tank containing Chemical Y would look like:
$16 \frac{2}{3}=3.2h \\ 16 \frac{2}{3}=3 \frac {2}{10}h$
We would now divide both sides by 3 2/10:
$\frac{16 \frac{2}{3}}{3 \frac{2}{10}}= \frac{3 \frac{2}{10}h}{3 \frac{2}{10}}$
This is the same as:
$\frac{\frac{50}{3}}{\frac{32}{10}}=h \\ \\ \frac{50}{3}* \frac{10}{32}=h \\ \\ \frac{500}{96}$
So the height of the tank containing Chemical Y is 500/96 = 5 5/24 feet.

8 0

2 years ago