Exponent Rules (with rational exponents)

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

•  $x^{\frac{4}{3}}y^{\frac{5}{2}}$  

•  $x^{\frac{2}{3}}y^{\frac{1}{2}}$  

•  $x^{\frac{1}{3}}y^{\frac{3}{2}}$  

•  $x^{\frac{2}{3}}y^{\frac{4}{3}}$  

Tags

CCSS.HSN.RN.A.1

CCSS.HSN.RN.A.2

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

•  $4v^{\frac{1}{3}}$  

•  $\frac{4}{v^{\frac{1}{3}}}$  

•  $\frac{v^{\frac{1}{3}}}{4}$  

•  $\frac{1}{4v^{\frac{1}{3}}}$  

Tags

CCSS.HSA.APR.A.1

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

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

•  $a^{\frac{1}{2}}b^{\frac{1}{2}}$  

•  $-\frac{1}{a^{\frac{1}{2}}b^{\frac{1}{2}}}$  

•  $-a^{\frac{1}{2}}b^{\frac{1}{2}}$  

Tags

CCSS.HSN.RN.A.2

Simplify . Your answer should contain only positive exponents.  $\left(x^{\frac{5}{3}}y^{-2}\right)^0$  

•  $1$  

•  $\frac{x^{\frac{5}{3}}}{y^2}$  

•  $x^{\frac{5}{3}}y^2$  

•  $\frac{y^2}{x^{\frac{5}{3}}}$  

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

CCSS.HSN.RN.A.2

Simplify . Your answer should contain only positive exponents.  $\frac{a^2b^0}{3a^4}$  

•  $1$  

•  $\frac{1}{3a^2}$  

•  $\frac{a^2}{3a^4}$  

•  $\frac{1}{3a^4}$  

Tags

CCSS.6.EE.A.2

CCSS.6.EE.A.3

CCSS.6.EE.B.6

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

•  $\frac{y^{\frac{25}{12}}}{x^{\frac{5}{6}}}$  

•  $\frac{x^{\frac{5}{6}}}{y^{\frac{25}{12}}}$  

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

•  $\frac{y^{\frac{17}{12}}}{x^{\frac{5}{6}}}$  

Tags

CCSS.HSA.APR.A.1

Simplify . Your answer should contain only positive exponents.  $\left(x^0y^{\frac{1}{3}}\right)^{\frac{3}{2}}x^0$  

•  $y^{\frac{1}{2}}$  

•  $1$  

•  $y^{\frac{4}{3}}$  

•  $0$  

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

CCSS.HSN.RN.A.2

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

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

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

•  $a^{\frac{3}{4}}b^{\frac{7}{4}}$  

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

Tags

CCSS.HSA.APR.D.7

CCSS.HSN.RN.A.1

CCSS.HSN.RN.A.2

Simplify . Your answer should contain only positive exponents.  $u^{-\frac{5}{4}}v^2•\left(u^{\frac{3}{2}}\right)^{-\frac{3}{2}}$  

•  $\frac{v^2}{u^{\frac{7}{2}}}$  

•  $\frac{v^2}{u^{\frac{5}{2}}}$  

•  $\frac{v^2}{u^{\frac{5}{4}}}$  

•  $v^2$  

Tags

CCSS.HSN.RN.A.2

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

•  $\frac{3y^{\frac{1}{12}}}{2}$  

•  $\frac{3y^{\frac{19}{12}}}{2}$  

•  $\frac{3}{2y^{\frac{1}{12}}}$  

•  $\frac{3}{2y^{\frac{19}{12}}}$  

Tags

CCSS.HSA.APR.D.6

CCSS.HSA.APR.D.7

CCSS.HSA.SSE.B.3

CCSS.HSN.RN.A.1

CCSS.HSN.RN.A.2