Question

Help Please! What is the simplest form of the product? ^3 sqrt 4x^2 * ^3 sqrt 8x^7

Answer 1

Answer:

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

Step-by-step explanation:

We have been given an expression $\sqrt[3]{4x^2} *\sqrt[3]{8x^7}$ and we are asked to find the product of our given expression.

Using exponent rule of power to powers $(a^{mn}=(a^m)^n)$ we can write $8x^7$ as $(2x^2)^3x$ and $4x^2=(2x)^2$.

Upon substituting these values in our expression we will get,

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

Using exponent rule $\sqrt[n]{x^m} =x^{\frac{m}{n}}$ we will get,

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

Multiplying $\sqrt[3]{x}$ by $\sqrt[3]{4x^2}$ we will get,

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

Using exponent rule $\sqrt[n]{x^m} =x^{\frac{m}{n}}$ we will get,

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

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

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

Therefore, the simplest form of the product of our given expression will be $2x^3\sqrt[3]{4}$.

Answer 2

Answer:

1. D

2. C

3. A

4. B

5. D

Step-by-step explanation: