What is 9×9 and 10×80

which of the following is equivalent to 3 sqrt 32x^3y^6 / 3 sqrt 2x^9y^2 where x is greater than or equal to 0 and y is greater

Nutka1998 [239]

Answer:

$\frac{\sqrt[3]{16y^4}}{x^2}$

Step-by-step explanation:

The options are missing; However, I'll simplify the given expression.

Given

$\frac{\sqrt[3]{32x^3y^6}}{\sqrt[3]{2x^9y^2} }$

Required

Write Equivalent Expression

To solve this expression, we'll make use of laws of indices throughout.

From laws of indices $\sqrt[n]{a} = a^{\frac{1}{n}}$

So,

$\frac{\sqrt[3]{32x^3y^6}}{\sqrt[3]{2x^9y^2} }$ gives

$\frac{(32x^3y^6)^{\frac{1}{3}}}{(2x^9y^2)^\frac{1}{3}}$

Also from laws of indices

$(ab)^n = a^nb^n$

So, the above expression can be further simplified to

$\frac{(32^\frac{1}{3}x^{3*\frac{1}{3}}y^{6*\frac{1}{3}})}{(2^\frac{1}{3}x^{9*\frac{1}{3}}y^{2*\frac{1}{3}})}$

Multiply the exponents gives

$\frac{(32^\frac{1}{3}x*y^{2})}{(2^\frac{1}{3}x^{3}*y^{\frac{2}{3}})}$

Substitute $2^5$ for 32

$\frac{(2^{5*\frac{1}{3}}x*y^{2})}{(2^\frac{1}{3}x^{3}*y^{\frac{2}{3}})}$

$\frac{(2^{\frac{5}{3}}x*y^{2})}{(2^\frac{1}{3}x^{3}*y^{\frac{2}{3}})}$

From laws of indices

$\frac{a^m}{a^n} = a^{m-n}$

This law can be applied to the expression above;

$\frac{(2^{\frac{5}{3}}x*y^{2})}{(2^\frac{1}{3}x^{3}*y^{\frac{2}{3}})}$ becomes

$2^{\frac{5}{3}-\frac{1}{3}}x^{1-3}*y^{2-\frac{2}{3}}$

Solve exponents

$2^{\frac{5-1}{3}}*x^{-2}*y^{\frac{6-2}{3}}$

$2^{\frac{4}{3}}*x^{-2}*y^{\frac{4}{3}}$

From laws of indices,

$a^{-n} = \frac{1}{a^n}$ ; So,

$2^{\frac{4}{3}}*x^{-2}*y^{\frac{4}{3}}$ gives

$\frac{2^{\frac{4}{3}}*y^{\frac{4}{3}}}{x^2}$

The expression at the numerator can be combined to give

$\frac{(2y)^{\frac{4}{3}}}{x^2}$

Lastly, From laws of indices,

$a^{\frac{m}{n} = \sqrt[n]{a^m}$ ; So,

$\frac{(2y)^{\frac{4}{3}}}{x^2}$ becomes

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

$\frac{\sqrt[3]{16y^4}}{x^2}$

Hence,

$\frac{\sqrt[3]{32x^3y^6}}{\sqrt[3]{2x^9y^2} }$ is equivalent to $\frac{\sqrt[3]{16y^4}}{x^2}$

8 0

3 years ago

In the diagram below DE is parallel to XY. What is the value of y?

jeka94

it would be 94 hope this helps

7 0

3 years ago

Read 2 more answers

Which segment is parallel to ED?

Jobisdone [24]

Answer:

AB

Step-by-step explanation:

The segments that are parallel need to be in the same direction ( up and down)

The segments that are parallel are FH, AB, GC

3 0

2 years ago

Read 2 more answers

Write an exponential function to represent a person consuming a bag of candy in which the initial value in an is 175 pieces and

Alisiya [41]

We will see that the exponential decay function is:

f(x) = 175*(0.8)^x

<h3>How to find the exponential decay?</h3>

The general exponential decay is:

f(x) = A*(1- r)^x

Where:

A is the initial value.
r is the rate of decay in decimal form.
x is the variable, in this case is the time.

Here we know that the initial value is 175, and the rate of decay is 20%. To get this in decimal form, we just divide it by 100%.

20%/100% = 0.2

Replacing that in the exponential function, we get:

f(x) = 175*(1 - 0.2)^x

f(x) = 175*(0.8)^x

If you want to learn more about exponential functions, you can read:

brainly.com/question/11464095

5 0

2 years ago

Is this right? if it isn't, what IS right?

umka2103 [35]

Answer:

You are wrong and the correct answer is vaunted.

Step-by-step explanation:

Why? Because it would be the only applicable word for this sentence.

Omnipotent: Having unlimited power; able to do anything.

Overt: One or shown openly; plainly or readily apparent, not secret or hidden.

Annihilated: Destroy utterly; obliterate.

Vaunted: Praised or boasted about, especially in an excessive way.

6 0

2 years ago