Question

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

Answer 1

Hi there!

This should be easy,lol!

Answer:

$\sqrt[3]{-128} = \boxed{-128 \sqrt{3} }$ (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 2

Answer:

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!