Question

Which expression is equivalent to ^3 square root 64a^6 b^7 c^9

Answer 1

Answer:

$4a^{2} b^{2} c^{3} (\sqrt[3]{b})$

Step-by-step explanation:

The given expression is :

$\sqrt[3]{(64}a^{6}b^{7} c^{9} )$

Writing 64 ,a,b,c as cubes we have:

= $\sqrt[3]{(}4^{3}( a^{2})^3( b^{2})^3.b( c^{3} )^3)$

Using radical rule we have :

=$4a^{2} b^{2} c^{3} (\sqrt[3]{b})$.

The second option is the right answer.

Answer 2

Answer:

$\sqrt[3]{64a^6b^7c^9}\Rightarrow 4a^2b^2c^3\sqrt[3]{b}$.

Option 2 is correct.

Step-by-step explanation:

Given: $\sqrt[3]{64a^6b^7c^9}$

We need to simplify the complex radical and to compare with given options which is equivalent to this.

$\Rightarrow \sqrt[3]{64a^6b^7c^9}$

separate the radical 3 with each term inside the radical.

$\Rightarrow \sqrt[3]{64}\cdot \sqrt[3]{a^6}\cdot \sqrt[3]{b^7}\cdot \sqrt[3]{c^9}$

Simplify each radical

$\Rightarrow 4\cdot a^2\cdot b^2\sqrt[3]{b}\cdot c^3$

Write all term together

$\Rightarrow 4a^2b^2c^3\sqrt[3]{b}$

Hence, The equivalent expression $\Rightarrow 4a^2b^2c^3\sqrt[3]{b}$