Question

What is the following product? RootIndex 3 StartRoot 16 x Superscript 7 Baseline EndRoot times RootIndex 3 StartRoot 12 x Superscript 9 Baseline EndRoot x squared (RootIndex 3 StartRoot 28 x squared EndRoot) x Superscript 5 Baseline (RootIndex 3 StartRoot 28 x EndRoot) 4 x squared (RootIndex 3 StartRoot 3 x squared EndRoot) 4 x Superscript 5 Baseline (RootIndex 3 StartRoot 3 x EndRoot)

Answer 1

D (4x^5(3sqrt3x)

Explanation:

Answer 2

`\sqrt[3]{16x^7} * \sqrt[3]{12x^9} = {4 x^(5)\sqrt[3]{3x} }`

Explanation:

Given

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

Required

Find the products

From laws of indices;

`\sqrt[m]{a} * \sqrt[m]{b} = \sqrt[m]{a*b}`

So;

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

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

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

From laws of indices

`a^m * a^n = a^(m+n); So,`

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

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

Expand 16 * 12

`\sqrt[3]{16x^7} * \sqrt[3]{12x^9} = \sqrt[3]{4*4*4*3* x^(16)}`

`\sqrt[3]{16x^7} * \sqrt[3]{12x^9} = \sqrt[3]{4^3 *3* x^(16)}`

From laws of imdices

`a^{(1)/(m)} = \sqrt[m]{a}`

So;

`\sqrt[3]{16x^7} * \sqrt[3]{12x^9} = {4^3 *3* x^(16)})^{(1)/(3)}`

`\sqrt[3]{16x^7} * \sqrt[3]{12x^9} = {4^{3*{(1)/(3)}} *3^{{(1)/(3)}}* x^{16*{(1)/(3)}}})`

`\sqrt[3]{16x^7} * \sqrt[3]{12x^9} = {4 *3^{{(1)/(3)}}* x^{(16)/(3)}}`

Divide 16 by 3 (Write as ,mixed number)

`\sqrt[3]{16x^7} * \sqrt[3]{12x^9} = {4 *3^{{(1)/(3)}}* x^{5(1)/(3)}}`

Split mixed numbers

`\sqrt[3]{16x^7} * \sqrt[3]{12x^9} = {4 *3^{{(1)/(3)}}* x^{5+(1)/(3)}}`

Apply law of indices

`\sqrt[3]{16x^7} * \sqrt[3]{12x^9} = {4 *3^{{(1)/(3)}}* x^(5)*{x ^(1)/(3)}}`

Reorder

`\sqrt[3]{16x^7} * \sqrt[3]{12x^9} = {4 * x^(5)*3^{{(1)/(3)}}*{x ^(1)/(3)}}`

`\sqrt[3]{16x^7} * \sqrt[3]{12x^9} = {4 x^(5)*3^{{(1)/(3)}}*{x ^(1)/(3)}}`

Apply law of indices

`\sqrt[3]{16x^7} * \sqrt[3]{12x^9} = {4 x^(5)*\sqrt[3]{3} *\sqrt[3]{x} }`

`\sqrt[3]{16x^7} * \sqrt[3]{12x^9} = {4 x^(5)*\sqrt[3]{3*x} }`

`\sqrt[3]{16x^7} * \sqrt[3]{12x^9} = {4 x^(5)*\sqrt[3]{3x} }`

`\sqrt[3]{16x^7} * \sqrt[3]{12x^9} = {4 x^(5)\sqrt[3]{3x} }`