Mathematics, 11.10.2020 08:01 fluffypuppies24

Giving brainliest to the answer who gives step by step examples clearly! Simplifying radicals
I am confused on how to get the answer, i believe it is the cubed that is throwing me off on both of these answers, please solve and use step by step? Thanks!

Giving brainliest to the answer who gives step by step examples clearly!

Simplifying radicals
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Answers: 1

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Answers

Answer from: Wolfb21345

Hi there!

This should be easy,lol!

$\sqrt[3]{-128} = \boxed{-128 \sqrt{3} }$ (Decimal: -221.702503)

$\sqrt[3]{162} = \boxed{162 \sqrt{3} }$ (Decimal: 280.592231)

$\sqrt[3]{-1000x^4} = \boxed{-1732.050808x^4}$

Sorry bout the explanation thingy. Their really long -.-!

But the last one is short so i'll put it for you!

Step-by-step explanation:

∴!For the last one!∴

$\sqrt[3]{-1000x^4}$

Simplifies to:

= - 1732.050808 * x^4

= - 1732.050808 * ( x * x * x * x)

= - 1732.050808x^4

Have a great day/night!

Answer from: milan44

10)

$=-4\sqrt[3]{2}$

12)

$=3\sqrt[3]6$

14)

$=-10x\sqrt[3]{x}$

Step-by-step explanation:

10)

We have:

$\sqrt[3]{-128}$

We want to simplify the cube root. So, let's start picking at the factors.

Notice that -128 is divisible by 64. So:

$=\sqrt[3]{-1\cdot64\cdot2}$

Now, notice that 64 is the same as 4³. (-1) is also the same as (-1)³. Therefore:

$=\sqrt{(-1)^3\cdot(4)^3\cdot2$

We can now expand our root:

$=\sqrt[3]{(-1)^3}\cdot\sqrt[3]{(4)^3}\cdot\sqrt[3]{2}$

The cubes and the cube roots cancel each other out. This leaves us with:

$=(-1)\cdot(4)\cdot\sqrt[3]2$

Simplify:

$=-4\sqrt[3]{2}$

12)

We have:

$\sqrt[3]{162}$

Again, let's see what we can factor out.

If it's unclear what we can factor out, we can guess and check. Since 162 is even, let's divide it by 2. This yields:

$=\sqrt[3]{2\cdot81}$

Notice here that 81 is the same as 3⁴. Therefore:

$=\sqrt[3]{2\cdot3^4}$

We can separate the 3 from the exponent using the properties of exponents:

$=\sqrt[3]{2\cdot3\cdot3^3}$

Expand:

$=\sqrt[3]{3^3}\cdot\sqrt[3]{2\cdot3}$

The cube roots and cube will cancel. This leaves us with:

$=3\cdot\sqrt{2\cdot3}$

Simplify:

$=3\sqrt[3]6$

14)

We have:

$\sqrt[3]{-1000x^4}$

Notice here that 1000 is the same as 10³. Also, we can separate an x from the x⁴. Therefore:

$=\sqrt[3]{-1\cdot (10)^3\cdot x^3\cdot x}$

Also, (-1) is the same as (-1)³. Thus:

$=\sqrt[3]{(-1)^3\cdot (10)^3\cdot x^3\cdot x}$

Expand:

$=\sqrt[3]{(-1)^3}\cdot\sqrt[3]{(10)^3}\cdot\sqrt[3]{x^3}\cdot\sqrt[3]{x}$

The cube roots and the cube will cancel. This leaves us with:

$=-1\cdot10\cdot x\cdot\sqrt[3]{x}$

Simplify:

$=-10x\sqrt[3]{x}$

And we're done!

Answer from: Quest

i = 2 / - 5

step-by-step explanation:

evaluation of ( 2 - 4 ) ( p + q ) when p = 2 and q = 5 i, by putting values of p and q,

0 = ( 2 - 4 ) ( p + q )0 = ( 2 - 4 ) ( 2 + 5 i ), by multiplying these0 = ( 4 + 10 i - 8 - 20 i )0 = 4 - 8 + 10 i - 20 i0 = - 4 -10 i 0 = 2 ( - 2 - 5 i )0 / 2 = - 2 - 5 i- 2 - 5 i = 0- 5 i = 2i = 2 / - 5

Answer from: Quest

use the power rule

( a b ) n = a n b n

to distribute the exponent.

apply the product rule to

3 x 2 y 3 . ( 3 x 2 ) 2 ( y 3 ) 2

apply the product rule to

3 x 2 . 3 2 ( x 2 ) 2 ( y 3 ) 2

raise

to the power of

2 . 9 ( x 2 ) 2 ( y 3 ) 2 multiply the exponents in ( x 2 ) 2

apply the power rule and multiply exponents,

( a m ) n = a m n . 9 x 2 ⋅ 2 ( y 3 ) 2

multiply

2 by 2 . 9 x 4 ( y 3 ) 2

multiply the exponents in

( y 3 ) 2 .

apply the power rule and multiply exponents,

( a m ) n = a m n . 9 x 4 y 3

⋅

multiply

3 by 2 . 9 x 4 y 6

step-by-step explanation:

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