##### Notes

This printable supports Common Core Mathematics Standard HSN-RN.A.2

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# Radicals and Rational Exponents (Grades 11-12)

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## Radicals and Rational Exponents

1.
Simplify. $root3(27x^10)$
1. $27x^10$
2. $root3(27x^10)$
3. $3root3(x^10)$
4. $(3x^3)root3x$
2.
If a field is $3 root(5)(x^8)$ units long and it is divided into $12 root(3)(x^4)$ segments, how long is each segment?
1. $1/4 sqrt(x^4)$
2. $-9 root(2)(x^4)$
3. $1/4 root (15)(x^4)$
4. $1/4 root(5/3)(x^2)$
3.
Express the following expression in simplest radical form using only one radical sign.

$9^(1/2)*x^(3/2)*y^(5/4)$

4.
An oval is $1/2 root(5)(x^2y^3)$ meters long. If a Kara completes $5 root(3)(x^2y)$ laps, how many meters has she run? Give your answer in simplified radicals.
1. $5/2x root(15)(xy^14)$
2. $5/2x root(3)(xy^14)$
3. $5 root(3)(xy^30)$
4. $2x root(15)(xy^14)$
5.
What is the ratio of $3 root(3)(x^2) sqrt(y^3)$ to $4 sqrt(x^3) root(3)(y^2)$ in the form __:1? Give your answer in the form of a radical.

6.
Write the ratio of $4 root(3)(x^4)$ to $2sqrt(x^5)$ in the form __:1. Show all of your work.

7.
Express each of the following with fractional exponents.

a. $root3(25^2)$

b. $sqrt35$

8.
If a field is $5 root(3)(x^2)$ units long and it is divided into $10 root(4)(x^5)$ segments, how long is each segment?

9.
Express the following expression in simplest radical form using only one radical sign.
$27^(1/3)*x^(4/5)*y^(2/5)*z^(1/5)$

10.
Simplify.

$(16x^4)^(3/2)$
1. $64x^6$
2. $4x^6$
3. $64x^10$
4. $4x^10$
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