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horsena [70]
2 years ago
5

What is the cube root of -729a9b6

Mathematics
2 answers:
Tema [17]2 years ago
7 0

Answer:

-9a3b2

Step-by-step explanation:

Harman [31]2 years ago
3 0

<u>ANSWER</u>

\sqrt[3]{- 729{a}^{9}  {b}^{6} }  =  - 9 {a}^{3} {b}^{2}

<u>EXPLANATION</u>

We want to find the cube root of

- 729 {a}^{9}  {b}^{6}

We express this symbolically as:

\sqrt[3]{- 729 {a}^{9}  {b}^{6} }

The expression under the radical called the radicand.

We need to express this radical in exponential form using the property,

{x}^{ \frac{m}{n} }  =  \sqrt[n]{ {x}^{m} }

Applying this rule gives us:

\sqrt[3]{- 729 {a}^{9}  {b}^{6} }  =  ({- 729 {a}^{9}  {b}^{6}})^{ \frac{1}{3} }

\sqrt[3]{- 729{a}^{9}  {b}^{6} }  =  ({- {9}^{3}  {a}^{9}  {b}^{6}})^{ \frac{1}{3} }

Recall that

({a}^{m} )^{n} = {a}^{mn}

We apply this rule on the RHS to get,

\sqrt[3]{- 729{a}^{9}  {b}^{6} }  =  ({- {9}^{3 \times { \frac{1}{3} } }  {a}^{9 \times { \frac{1}{3} } }  {b}^{6 \times { \frac{1}{3} } }})

This simplifies to

\sqrt[3]{- 729{a}^{9}  {b}^{6} }  =  - 9 {a}^{3} {b}^{2}

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