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What is the following product 3 square root 16 x7 times3 square root 12 x9

1 Answer

2 votes

Answer:


4x^5\sqrt[3]{3x}

Explanation:

The product will be written as:


\sqrt[3]{16x^7}*\sqrt[3]{12x^9}

As both the radicals have same root 3 so,


= \sqrt[3]{16x^7 * 12x^9}

The powers of x will be added as the base is same


=\sqrt[3]{16*12 * x^((7+9))}\\=\sqrt[3]{192x^(16)}\\

We have to break the terms so that the powers can be written as a multiple of 3


=\sqrt[3]{64*3*x^(15)*x}\\ =\sqrt[3]{(4^3)*3*(x^(3*5))*x}\\ Applying\ cube\ root\\= 4x^5\sqrt[3]{3x}

User Brenda
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