Which expression is equivalent to ^4sqrt6/^3sqrt2?

2 answers:

4 0

$\dfrac{\sqrt[4]6}{\sqrt[3]2}=6^\frac{1}{4}:2^\frac{1}{3}=6^\frac{1\cdot3}{4\cdot3}:2^{\frac{1\cdot4}{3\cdot4}}=6^\frac{3}{12}:2^\frac{4}{12}=(6^3)^\frac{1}{12}:(2^4)^\frac{1}{12}\\\\=216^\frac{1}{12}:16^\frac{1}{12}=(216:16)^\frac{1}{12}=\sqrt[12]{\dfrac{216}{16}}=\sqrt[12]{\dfrac{27}{2}}\\\\\text{Answer:}\ 1)\ \sqrt[12]{\dfrac{27}{2}}$

anzhelika [568]3 years ago

3 0

Answer:

A!!!!!

Step-by-step explanation:

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The number of apples in a box decreased from 150 to 135. What is the percent decrease of the number of apples in the box?

goblinko [34]

Answer:

10% decrease

Step-by-step explanation:

The formula for percent change is:

$\frac{\textrm{New}-\textrm{Old}}{\textrm{Old}} \times 100$

Therefore, for this example:

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5 0

3 years ago

Write an equation of the line that passes through (2001, 35) and (2004.5, 16.1 ) points

Allisa [31]

Answer: If you are looking for Slope-Intercept form (y=mx+b), It would be...

y=-5.4x+10840.4.

If you are looking for Point-Slope form, it would be...

y=-5.4x+10840.4.

Step-by-step explanation: Write in Slope-Intercept from, y=mx+b.

Point-Slope form : Use the Point-Slope formula, y-y1=m(x-x1) to find the equation of the line.

I hope this helps you out! ☺

7 0

3 years ago

WHAT IS THE REMAINDER WHEN <img src="https://tex.z-dn.net/?f=32%5E%7B37%5E%7B32%7D%20%7D" id="TexFormula1" title="32^{37^{32} }"

Feliz [49]

Recall Euler's theorem: if $\gcd(a,n) = 1$ , then

$a^{\phi(n)} \equiv 1 \pmod n$

where $\phi$ is Euler's totient function.

We have $\gcd(9,32) = 1$ - in fact, $\gcd(9,32^k)=1$ for any $k\in\Bbb N$ since $9=3^2$ and $32=2^5$ share no common divisors - as well as $\phi(9) = 6$ .

Now,

$37^{32} = (1 + 36)^{32} \\\\ ~~~~~~~~ = 1 + 36c_1 + 36^2c_2 + 36^3c_3+\cdots+36^{32}c_{32} \\\\ ~~~~~~~~ = 1 + 6 \left(6c_1 + 6^3c_2 + 6^5c_3 + \cdots + 6^{63}c_{32}\right) \\\\ \implies 32^{37^{32}} = 32^{1 + 6(\cdots)} = 32\cdot\left(32^{(\cdots)}\right)^6$