Explain why the radical expression is or is NOT in simplified form?

The expression is not in simplified form because a radical appears in the denominator of a fraction.

The expression is simplified because the radicand contains no fractions

The expression is simplified because the radicand has no perfect-square factors other than 1.

The expression is not simplified because it contains a fraction.

Simplify . Your answer should contain only positive exponents. y x 1 3 ⋅ x y 3 2 yx^{\frac{1}{3}}\cdot xy^{\frac{3}{2}} y x 3 1 ⋅ x y 2 3

x 4 3 y 5 2 x^{\frac{4}{3}}y^{\frac{5}{2}} x 3 4 y 2 5

x 2 3 y 1 2 x^{\frac{2}{3}}y^{\frac{1}{2}} x 3 2 y 2 1

x 1 3 y 3 2 x^{\frac{1}{3}}y^{\frac{3}{2}} x 3 1 y 2 3

x 2 3 y 4 3 x^{\frac{2}{3}}y^{\frac{4}{3}} x 3 2 y 3 4

Simplify . Your answer should contain only positive exponents. 4 v 2 3 ⋅ v − 1 4v^{\frac{2}{3}}\cdot v^{-1} 4 v 3 2 ⋅ v − 1

4 v 1 3 \frac{4}{v^{\frac{1}{3}}} v 3 1 4

4 v 1 3 4v^{\frac{1}{3}} 4 v 3 1

v 1 3 4 \frac{v^{\frac{1}{3}}}{4} 4 v 3 1

1 4 v 1 3 \frac{1}{4v^{\frac{1}{3}}} 4 v 3 1 1

Simplify . Your answer should contain only positive exponents. ( a 1 2 b 1 2 ) − 1 \left(a^{\frac{1}{2}}b^{\frac{1}{2}}\right)^{-1} ( a 2 1 b 2 1 ) − 1

1 a 1 2 b 1 2 \frac{1}{a^{\frac{1}{2}}b^{\frac{1}{2}}} a 2 1 b 2 1 1

a 1 2 b 1 2 a^{\frac{1}{2}}b^{\frac{1}{2}} a 2 1 b 2 1

− 1 a 1 2 b 1 2 -\frac{1}{a^{\frac{1}{2}}b^{\frac{1}{2}}} − a 2 1 b 2 1 1

− a 1 2 b 1 2 -a^{\frac{1}{2}}b^{\frac{1}{2}} − a 2 1 b 2 1

Simplify . Your answer should contain only positive exponents. 2 x 1 2 y 1 3 2 x 4 3 y − 7 4 \frac{2x^{\frac{1}{2}}y^{\frac{1}{3}}}{2x^{\frac{4}{3}}y^{-\frac{7}{4}}} 2 x 3 4 y − 4 7 2 x 2 1 y 3 1

y 25 12 x 5 6 \frac{y^{\frac{25}{12}}}{x^{\frac{5}{6}}} x 6 5 y 1 2 2 5

x 5 6 y 25 12 \frac{x^{\frac{5}{6}}}{y^{\frac{25}{12}}} y 1 2 2 5 x 6 5

2 y 25 12 x 5 6 \frac{2y^{\frac{25}{12}}}{x^{\frac{5}{6}}} x 6 5 2 y 1 2 2 5

y 17 12 x 5 6 \frac{y^{\frac{17}{12}}}{x^{\frac{5}{6}}} x 6 5 y 1 2 1 7

Simplify . Your answer should contain only positive exponents. a 3 4 b − 1 ⋅ b 7 4 3 b − 1 \frac{a^{\frac{3}{4}}b^{-1}\cdot b^{\frac{7}{4}}}{3b^{-1}} 3 b − 1 a 4 3 b − 1 ⋅ b 4 7

a 3 4 b 7 4 3 \frac{a^{\frac{3}{4}}b^{\frac{7}{4}}}{3} 3 a 4 3 b 4 7

a 3 4 b 3 4 3 \frac{a^{\frac{3}{4}}b^{\frac{3}{4}}}{3} 3 a 4 3 b 4 3

a 3 4 b 7 4 a^{\frac{3}{4}}b^{\frac{7}{4}} a 4 3 b 4 7

3 a 3 4 b 7 4 3a^{\frac{3}{4}}b^{\frac{7}{4}} 3 a 4 3 b 4 7

Simplify . Your answer should contain only positive exponents. 3 y − 5 4 y − 1 • 2 y − 1 3 \frac{3y^{-\frac{5}{4}}}{y^{-1}•2y^{-\frac{1}{3}}} y − 1 • 2 y − 3 1 3 y − 4 5

3 y 1 12 2 \frac{3y^{\frac{1}{12}}}{2} 2 3 y 1 2 1

3 y 19 12 2 \frac{3y^{\frac{19}{12}}}{2} 2 3 y 1 2 1 9

3 2 y 1 12 \frac{3}{2y^{\frac{1}{12}}} 2 y 1 2 1 3

3 2 y 19 12 \frac{3}{2y^{\frac{19}{12}}} 2 y 1 2 1 9 3

Simplify . Your answer should contain only positive exponents. ( 6 b ) − 4 3 \left(6b\right)^{\frac{-4}{3}} ( 6 b ) 3 − 4

1 6 4 3 b 4 3 \frac{1}{6^{\frac{4}{3}}b^{\frac{4}{3}}} 6 3 4 b 3 4 1

6 b 4 3 \frac{6}{b^{\frac{4}{3}}} b 3 4 6

b 4 3 6 \frac{b^{\frac{4}{3}}}{6} 6 b 3 4

6 4 3 b 4 3 \frac{6^{\frac{4}{3}}}{b^{\frac{4}{3}}} b 3 4 6 3 4

Radicals & Rational Exponents

Authored by Brandy Stapleton

Mathematics

11th Grade

CCSS covered

Used 2+ times

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47 questions

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MULTIPLE CHOICE QUESTION

1 min • 1 pt

Rewrite the following
∛x⁵

x^3/5

x^5/3

x²

x³⋅x⁵

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

Write in exponential form
∜(3x)³

3x³⁄ ⁴

(3x)³∕ ⁴

(3x)⁴⁄ ³

3x⁴⁄ ³

Write as a radical expression
y²⁄ ³

2y³

√y³

∛y²

3y²

∜m³ is the same as which answer?

m^3/4

m¹²

m^4/3

m⁷

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

Write as a radical expression
y¹⁄ ³

∛y

y³

√y

1∕ 3y

Simplify

3 x² y² z √3yz

3 x y z √xy²

3xyz

Can't Simplify

MULTIPLE CHOICE QUESTION

1 min • 1 pt

11√5

11√10

5√5

12√10

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