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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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Express without a radical and with positive fractional exponents.

$5sqrt(x^-1y^-1$
1. $5x^(1/2)y^(1/2)$
2. $(xy)/5$
3. $5*(x^(1/2)y^(1/2))$
4. $5/{x^(1/2)y^(1/2)}$
5. None of the above
Simplify the radical expression. $root3 63 * root3 9$
1. $6root3 9$
2. $3 root3 21$
3. $3 root3 15$
4. $6 root3 21$
Simplify. $root2 18 + 2 root2 8$
1. $7root2 2$
2. $3root2 2+4root2 2$
3. $11root2 2$
4. $7$
Simplify.

$7sqrt2+3sqrt2$
1. $20$
2. $10sqrt2$
3. $21sqrt2$
4. $84$
Express with positive rational exponents.

$2root{4}(64 x^6 y^(-8) z^(-12))$
1. $2^(5/2) x^(3/2) y^2 z^3$
2. $(4x \ (2x)^(1/2)) / (y^2 z^3)$
3. $(4x^2 ) / (y^4 z^8)$
4. $(16 x^3) / (y^4 z^6)$
Simplify.
$sqrt28$
1. $4sqrt7$
2. $4sqrt2$
3. $2sqrt7$
4. $7sqrt2$
5. $3sqrt4$
Simplify the radical expression. $sqrt {:245x^7y^8$
1. $(7y^4)sqrt {:5x^7$
2. $(7x^7y^8)sqrt {:5x$
3. $(7x^3y^4)sqrt {:5x$
4. $(7x^3y^4)sqrt5$
The expression $sqrt(200)$ is equivalent to which of the following?
1. $25sqrt(8)$
2. $2sqrt(10)$
3. $100sqrt(2)$
4. $10sqrt(2)$
1. $sqrt98$
2. $sqrt72$
3. $sqrt110$
4. $sqrt120$
Simplify.

$root6(d^24x^36)$
1. $d^6x^4$
2. $d^30x^12$
3. $d^(1/4)x^(1/6)$
4. $d^4x^6$
$(3x)^(2/3) y^(1/3)$
1. $root{3}{9x^2y}$
2. $(sqrt(27x^3)) / (y^3)$
3. $root{3}{3x^2y^3}$
4. $root{3}{9xy}$