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# Common Core Standard HSN-RN.A.2 Questions

Rewrite expressions involving radicals and rational exponents using the properties of exponents.

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Simplify: $(32a^4b^2)/(8a^3b^2).$ Choose the best answer.
1. $4ab^0$
2. $4a$
3. $(4)/(16ab^4)$
4. $4ab^4$
Simplify the expression: $-5y^3 + 2y^2 - 6y - 10y^2 + 10y^3 + y$
1. $5y^3 - 8y^2 - 5y$
2. $-5y^3 + 8y^2 + 5y$
3. $15y^3 + 12y^2 + 7y$
4. $-15y^3 - 12y^2 - 7y$
Simplify $(a)/(b^2) * (b^3)/(a).$
1. $a^2b^5$
2. $a^0b^1$
3. $b$
4. $b^3$
Evaluate the expression.

$(100)^(5/2)$
1. $(root5 32)^2$
2. $(root2 100)^5 = 100,000$
3. $(root5 100)^2$
4. $(10^2)^5 = 10^10 = 10,000,000,000$
Express the following in simplest radical form using only one radical sign.

$9^(1/2)*x^(3/2)*y^(5/4)$
1. $9sqrt(x^3y^(5/2))$
2. $3sqrt(x^3y^(5))$
3. $3sqrt(x^3y^(5/2))$
4. $sqrt(9x^3y^(5))$
Express with fractional exponents.

$root3(25^2)$
1. $25^(2/3)$
2. $5^(3)$
3. $root()(25^(3)$
4. $25^(3/2)$
Express the following in simplest radical form using only one radical sign.
$27^(1/3)*x^(4/5)*y^(2/5)*z^(1/5)$
1. $3root5(x^4y^2z)$
2. $27root15(x^4y^2z)$
3. $root5(3x^4y^2z)$
4. $1/(3root5(x^4y^2z))$
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. $2x root(15)(xy^14)$
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? Your answer should be in the form of a radical.
1. $3y^(5/6):4x^(5/6)$
2. $(3y^(5/6))/(4x^(5/6)):1$
3. $(3root(6)(y^5))/(4root(6)(x^5)):1$
4. $3root(6)(y^5):4root(6)(x^5)$
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. $1/4 root(5/3)(x^2)$
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?
1. $2x^(7/12)$
2. $1/(2x^(7/12))$
3. $2x^(-7/12)$
4. $1/(1/2x^(7/12))$
Write the ratio of $4 root(3)(x^4)$ to $2sqrt(x^5)$ in the form __:1.
1. $8 root(6)(x^9):1$
2. $4 root(3)(x^4):2sqrt(x^5)$
3. $2 root(6)(x^7):1$
4. $2/(root(6)(x^7)):1$