Question

What is the following product? 3 sqrt 16x7 . 3 sqrt 12x9

Answer 1

Answer:  The required product is $4x^5\sqrt[3]{3x}$

Step-by-step explanation:  We are given to find the following product :

$P=\sqrt[3]{16x^7}\times \sqrt[3]{12x^9}.$

We will be using the following property of exponents :

$(i)~\sqrt[b]{x^a}=x^\frac{a}{b}\\\\(ii)~x^a\times x^b=x^{a+b}\\\\(iii)~x^a\times y^a=(xy)^a.$

The required multiplication is as follows :

$P\\\\=\sqrt[3]{16x^7}\times \sqrt[3]{12x^9}\\\\=(16x^7)^\frac{1}{3}\times (12x^9)^\frac{1}{3}\\\\=(16\times12\times x^{7+9})^\frac{1}{3}\\\\=(192x^{16})^\frac{1}{3}\\\\=192^\frac{1}{3}x^\frac{16}{3}\\\\=(64\times3)^\frac{1}{3}x^\frac{16}{3}\\\\=4^{3\times\frac{1}{3}}3^\frac{1}{3}x^{5+\frac{1}{3}}\\\\=4\times 3^\frac{1}{3}x^5\times x^\frac{1}{3}\\\\=4x^5\sqrt[3]{3x}.$

Thus, the required product is $4x^5\sqrt[3]{3x}.$

Answer 2

Answer:

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brainly.com/question/8567836