Question

Can i have step by step guidance how to simplify this

Answer 1

As given by the question

There are given that the expression

`6\sqrt[]{75x^9y^(12)z}`

Now,

Simplify the above expression

First, apply the radical rule;

`\sqrt[]{ab}=\sqrt[]{a}\sqrt[]{b}`

Then,

From the given expression

`6\sqrt[]{75x^9y^(12)z}=6\sqrt[]{75}\sqrt[]{x^9y^(12)z}^{}`

Then,

`6\sqrt[]{75}\sqrt[]{x^9y^(12)z}^{}=6\sqrt[]{75}\sqrt[]{x^9}\sqrt[]{y^(12)z}`

Now,

`6\sqrt[]{75}\sqrt[]{x^9}\sqrt[]{y^(12)z}=6*5\sqrt[]{3}\sqrt[]{x^9}\sqrt[]{y^(12)}\text{ }\sqrt[]{z}`

Then,

Simplify the above equation again

So,

`\begin{gathered} 6*5\sqrt[]{3}\sqrt[]{x^9}\sqrt[]{y^(12)}\text{ }\sqrt[]{z}=6*5\sqrt[]{3*}^{}\sqrt[]{x^8* x}*\sqrt[]{y^(12)}\sqrt[]{z} \\ =6*5\sqrt[]{3*}x^4\sqrt[]{x}*\sqrt[]{y^(12)}\sqrt[]{z} \end{gathered}`

Then,

Simplify the y terms in the above result

So,

`\begin{gathered} 6*5\sqrt[]{3*}x^4\sqrt[]{x}*\sqrt[]{y^(12)}\sqrt[]{z}=6*5\sqrt[]{3*}x^4\sqrt[]{x}* y^6\sqrt[]{z} \\ \end{gathered}`

Now,

Multiply 6 with 5 and written in the standard form

So,

`6*5\sqrt[]{3*}x^4\sqrt[]{x}* y^6\sqrt[]{z}=30x^4y^6\sqrt[]{x}\sqrt[]{z}`

Hence, the value of the given expression is shown below:

`30\sqrt[]{3}x^4y^6\sqrt[]{x}\sqrt[]{z}`