Expressions and Equations with Rational Exponents

When you multiply exponents with the same base you should _______ their exponents.

True or False. 3x⁰ when simplified equals 1.

• True

• False

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

•  $x^{\frac{4}{3}}y^{\frac{5}{2}}$  

•  $x^{\frac{2}{3}}y^{\frac{1}{2}}$  

•  $x^{\frac{1}{3}}y^{\frac{3}{2}}$  

•  $x^{\frac{2}{3}}y^{\frac{4}{3}}$  

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

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

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

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

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

Simplify
  $x^{\frac{2}{3}}$    ⋅   $x^{\frac{1}{3}}$  

• 2x

•  $x^{\frac{2}{9}}$  

• x

• x²

Simplify
 $\frac{x^{\frac{7}{8}}}{x}$  

•  $x^{\frac{1}{8}}$  

•  $\frac{1}{x^{\frac{1}{8}}}$  

•  $\frac{1}{8x}$  

• x⁴

Which is NOT the same as   $p^{\frac{2}{3}}$    ?

•  $\left(p^{\frac{1}{3}}\right)^2$  

• ∛p²

• (p²)^1/3

• √p³

Simplify    $\left(x^{\frac{2}{3}}\right)^{\frac{2}{5}}\$ 

•  $x^{\frac{4}{15}}$  

•  $x^{\frac{16}{15}}$  

• x⁶

• 6x

8

• W
• O
• R
• K

 $3^{\frac{1}{2}}\cdot\ 27^{\frac{1}{2}}$  Simplify the expression:

• 9

• 81

• 3

•  $\frac{1}{3}$