Question

What is the following product ^3sqrt16x^7*^3sqrt12x^9

Answer 1

Answer:

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

Step-by-step explanation:

Given

$\sqrt[3]{16x^7}\left(\sqrt[3]{12x^9}\right)\\\sqrt[3]{4^{2} x^7}\sqrt[3]{4(3)x^9}\\ 4^\frac{2}{3} . x^\frac{7}{3} . 4^\frac{1}{3} . 3^\frac{1}{3} . x^\frac{9}{3}\\ 4^\frac{2+1}{3} . 3^\frac{1}{3}. x^\frac{9+7}{3} \\4^\frac{3}{3} . 3^\frac{1}{3}. x^\frac{16}{3}\\ 4\sqrt[3]{3x^16}$

$4\sqrt[3]{3} . x^\frac{16}{3} \\4\sqrt[3]{3} . x^\frac{15}{3} .x^\frac{1}{3} \\4\sqrt[3]{3} . x^5 .x^\frac{1}{3} \\4x^5\sqrt[3]{3x}$ !

Answer 2

Answer:

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

Step-by-step explanation:

Given

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

Required

Products of both

To do this, we have to apply the laws of indices,

Follow the highlighted steps

Step 1: Multiply both parameters directly

Since they both have the same roots, they can be multiplied directly according to the law of indices

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

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

Step 2: Apply the 1st law of indices

First law of indices states that

$x^{a} * x^{b} = x^{a + b}$

So, $\sqrt[3]{16x^{7} * 12x^{9} }$ becomes

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

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

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

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

Step 3: Rewrite the expression

$\sqrt[3]{192 * x^{16} }$ = $({192 * x^{16} })^{\frac{1}{3} }$

Step 4: Expand the Expression in bracket

$({192 * x^{16} })^{\frac{1}{3} }$ = $({64 * 3* x^{15} * x^{1} })^{\frac{1}{3} }$

Break down into bits

$({192 * x^{16} })^{\frac{1}{3} }$ = $64^\frac{1}{3} * 3^\frac{1}{3} * (x^{15})^\frac{1}{3} * (x^{1})\frac{1}{3}$

$({192 * x^{16} })^{\frac{1}{3} }$ = $(4^{3}) ^\frac{1}{3} * 3^\frac{1}{3} * (x^{15})^\frac{1}{3} * (x^{1})\frac{1}{3}$

$({192 * x^{16} })^{\frac{1}{3} }$ = $(4^{3*\frac{1}{3}}) * 3^\frac{1}{3} * (x^{15}*^\frac{1}{3}) * (x^{\frac{1}{3}})$

$({192 * x^{16} })^{\frac{1}{3} }$ = $4 * 3^\frac{1}{3} * (x^{5}}) * (x^{\frac{1}{3}})$

$({192 * x^{16} })^{\frac{1}{3} }$ = $4 (x^{5}})* 3^\frac{1}{3} * (x^{\frac{1}{3}})$

$({192 * x^{16} })^{\frac{1}{3} }$ = $4x^{5}} * (3^\frac{1}{3} * x^{\frac{1}{3}})$

$({192 * x^{16} })^{\frac{1}{3} }$ = $4x^{5}} * (3x)^\frac{1}{3}$

$({192 * x^{16} })^{\frac{1}{3} }$ = $4x^{5}} * \sqrt[3]{3x}$

$({192 * x^{16} })^{\frac{1}{3} }$ = $4x^{5}} (\sqrt[3]{3x})$

Hence, the expression $\sqrt[3]{16x^{7} } * \sqrt[3]{12x^{9} }$ = $4x^{5}} (\sqrt[3]{3x})$