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# Common Core Standard HSN-RN.A.1 Questions

Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. For example, we define 51/3 to be the cube root of 5 because we want (51/3)3 = 5(1/3)3 to hold, so (51/3)3 must equal 5.

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What is the reciprocal of $b^4?$
1. $1/b^4$
2. $b^(-4)$
3. $1/(b^(-4)$
4. $b^(1/4)$
Evaluate the expression $3^(x + 2)$ when $x = -2$.
1. $1/3$
2. $1$
3. $3$
4. $81$
What is $root3( 27/125)$ in simplest form?
1. $(3 root3 5)/5$
2. $(3)/(root3 5)$
3. $(root3 5)/5$
4. $(3)/5$
Simplify $(4x^4y)^(3/2)$. Assume all variables are positive.
1. $4x^6y^(3/2)$
2. $8x^6y^(3/2)$
3. $4x^4y^(3/2)$
4. $2x^6y^(3/2)$
What is $root3 20 * root3 6$ in simplest form?
1. $root 3 120$
2. $2(root 2 15)$
3. $8(root 3 15)$
4. $2(root 3 15)$
Simplify $(x^2y)/(x^(3/4)y^(1/3)$
1. $x^(5/4)y^(2/3)$
2. $x^(11/14)y^(4/3)$
3. $x^(3/2)y^(1/3)$
4. $x^(1/2)y^(1/3)$
What is the solution of $5x^(2/3) - 7 = 13?$
1. $-4$
2. $4$
3. $8$
4. $20$