Question

help pls
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Answer 1

@Vocaloid

Answer 2

Multiply the exponents

Answer 3

ok

Answer 4

Distribute the exponent into the parenthesis by multiplying.

\(\Large\bf{x^{5 \times \frac{2}{3}}~y^{3 \times \frac{2}{3}}}\)

What does that simplify to?

Answer 5

x^10/3 y^2

Answer 6

Correct. Now since you have \(\large\bf{x^{\frac{10}{3}}}\) you would change this into radical form.

Follow by: \(\Large\bf{x^{\frac{m}{n}} = \sqrt[n]{x^{m}}}\)

So how would you turn \(\Large\bf{x^{\frac{10}{3}}}\) into radical?

Answer 7

3sqrt10

Answer 8

Correct. Now you need to split the \(\large\bf{x^{10}}\) into two terms that have one perfect square. If we add 9 and 1 we get 10, 9 is a perfect square so factor it out.

\(\Large\bf{\sqrt[3]{x^{10}} ~~\rightarrow ~~ \sqrt[3]{x^{9}x}}\)

Now we need to rewrite this so we can pull the term out.

`Remember if an exponent expression is brought the power of an exponent then the exponents will multiply`

So 9 `splits to 3 x 3`.

\(\Large\bf{\sqrt[3]{(x^{3})^{3}x}}\)

How would this simplify?

Answer 9

`Look at the exponent and the cube rooting, you see x is being brought to the power of 3 which cancels the cubing, meaning x^3 is brought out`

Answer 10

3√(x^27

Answer 11

Not quite.

`When an exponential expression is brought to the power of another exponent the exponents will multiply.`

So to simplify we had split \(\large\bf{x^{10}~~\rightarrow ~~x^{9}x}\)

But our exponent is cube rooted. So we split the \(\large\bf{x^{9}~~\rightarrow (x^{3})^{3}}\) because we need to take the term out.

So \(\Large\bf{\sqrt[3]{(x^{3})^{3}x} ~~\rightarrow ~~ x^{3}\sqrt[3]{x}}\)

`BECAUSE THE POWER OF 3 CANCELS OUT WITH THE CUBE ROOTING` (not shouting just pointing out cx)

So you end with...

\(\Large\bf{x^{3}y^{2}\sqrt[3]{x}}\)

Answer 12

thank youuu