Quiz about Rational Exponents

Question 1

Simplify. Your answer should contain only positive exponents with no rational exponents in the denominator.

$$\left(\frac{x^{\frac{1}{3}}y^{-1}\cdot\left(x^{\frac{3}{2}}y^{-\frac{3}{4}}\right)^{-\frac{2}{3}}}{x^{-\frac{3}{2}}y^{-\frac{4}{3}}}\right)^0$$

Accepted Answer

Answer

$$\frac{x^{\frac{1}{2}}y^{\frac{5}{8}}}{x^3}$$

Answer

$$\frac{y^{\frac{2}{3}}}{y}$$

Answer

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

Question 2

Simplify. Your answer should contain only positive exponents with no rational exponents in the denominator.

$$\frac{x^{-\frac{2}{3}}}{\left(\left(\left(y^{\frac{5}{4}}\right)^{\frac{5}{3}}\right)\cdot\left(x^{-\frac{1}{2}}y^{-\frac{3}{2}}\right)^{\frac{3}{4}}\right)^{\frac{2}{3}}}$$

Accepted Answer

$$\frac{x^{\frac{7}{12}}y^{\frac{13}{36}}}{xy}$$

Answer

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

Answer

$$\frac{x^{\frac{7}{6}}}{y}$$

Answer

$$\frac{x^4y^{\frac{7}{9}}}{y^7}$$

Question 3

Simplify. Your answer should contain only positive exponents with no rational exponents in the denominator.

$$\left(\frac{ba^{-\frac{1}{2}}\cdot a^{\frac{3}{2}}b^{-\frac{3}{2}}}{a^{\frac{3}{4}}b^{-1}}\right)^2$$

Accepted Answer

$$ba^{\frac{1}{2}}$$

Answer

$$b^4a^{\frac{7}{2}}$$

Answer

$$\frac{b^{\frac{7}{8}}}{b}$$

Answer

$$\frac{a^{\frac{2}{3}}b^{\frac{3}{4}}}{a^2}$$

Question 4

Simplify. Your answer should contain only positive exponents with no rational exponents in the denominator.

$$\frac{\left(xy^{-\frac{1}{4}}\right)^0}{x^0y^{\frac{1}{3}}\cdot x^{\frac{5}{4}}y^0}$$

Accepted Answer

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

Answer

$$\frac{y^{\frac{3}{4}}x^{\frac{9}{2}}}{y^2}$$

Answer

$$\frac{y^{\frac{1}{4}}}{x^2y^2}$$

Answer

$$x^3y^{\frac{53}{12}}$$

Question 5

Simplify. Your answer should contain only positive exponents with no rational exponents in the denominator.

$$\left(\frac{m^{-2}n^{\frac{1}{4}}\cdot m^{\frac{1}{4}}n^{-\frac{5}{3}}}{m}\right)^{\frac{1}{3}}$$

Accepted Answer

$$\frac{n^{\frac{19}{36}}m^{\frac{1}{12}}}{nm}$$

Answer

$$\frac{m^{\frac{3}{4}}n^{\frac{3}{4}}}{m^4n^3}$$

Answer

$$\frac{n^{\frac{1}{2}}m^{\frac{1}{2}}}{m^2}$$

Answer

$$\frac{m^{\frac{5}{8}}n^{\frac{5}{4}}}{m^2}$$

Question 6

Simplify. Your answer should contain only positive exponents with no rational exponents in the denominator.

$$\frac{\left(x^2y^2\cdot y^{-\frac{1}{2}}\right)^{-\frac{5}{3}}}{x^{\frac{5}{4}}y^{-\frac{7}{4}}}$$

Accepted Answer

$$\frac{x^{\frac{5}{12}}y^{\frac{1}{4}}}{x^5y}$$

Answer

$$\frac{y^{\frac{1}{6}}x^{\frac{2}{3}}}{x^2}$$

Answer

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

Answer

$$\frac{1}{y}$$

Question 7

Simplify. Your answer should contain only positive exponents with no rational exponents in the denominator.

$$\frac{\left(x^{\frac{7}{4}}\cdot x^{\frac{3}{2}}\cdot x^0y^{-1}\right)^{-\frac{2}{3}}}{\left(x^0y^{\frac{5}{3}}\right)^{-\frac{5}{3}}}$$

Accepted Answer

$$\frac{y^{\frac{31}{9}}x^{\frac{5}{6}}}{x^3}$$

Answer

$$\frac{xy^{\frac{5}{18}}}{y^2}$$

Answer

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

Answer

$$\frac{1}{y}$$

Question 8

Simplify. Your answer should contain only positive exponents with no rational exponents in the denominator.

$$\frac{xx^0\cdot x^2y^2}{\left(x^{-\frac{3}{2}}y^{\frac{2}{3}}\right)^{\frac{1}{2}}}$$

Accepted Answer

$$x^{\frac{15}{4}}y^{\frac{5}{3}}$$

Answer

$$\frac{y^{\frac{5}{12}}}{yx}$$

Answer

$$\frac{x^2y^{\frac{5}{6}}}{y^2}$$

Answer

$$\frac{y^{\frac{7}{4}}x^{\frac{1}{2}}}{x}$$

Question 9

Simplify. Your answer should contain only positive exponents with no rational exponents in the denominator.

$$\left(\frac{y^{\frac{5}{4}}}{\left(x^{-\frac{7}{4}}y^{\frac{3}{2}}\right)^2\cdot yx^{\frac{5}{4}}}\right)^{\frac{1}{2}}$$

Accepted Answer

$$\frac{y^{\frac{5}{8}}x^{\frac{9}{8}}}{y^2}$$

Answer

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

Answer

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

Answer

$$x^2y^{\frac{7}{2}}$$

Question 10

Simplify. Your answer should contain only positive exponents with no rational exponents in the denominator.

$$\frac{x^{-2}y^{-\frac{1}{2}}}{\left(x^{-\frac{5}{4}}\right)^{\frac{3}{2}}\cdot x^{\frac{4}{3}}y^{\frac{3}{4}}}$$

Accepted Answer

$$\frac{y^{\frac{3}{4}}x^{\frac{13}{24}}}{y^2x^2}$$

Answer

$$\frac{x^{\frac{31}{4}}y^{\frac{5}{6}}}{y^5}$$

Answer

$$\frac{y^{\frac{11}{12}}x^{\frac{1}{4}}}{x^3}$$

Answer

$$\frac{yx^{\frac{7}{24}}}{x}$$

Question 11

Simplify. Your answer should contain only positive exponents with no rational exponents in the denominator.

$$\frac{\left(x^0y^{\frac{7}{4}}\right)^{-\frac{1}{2}}}{xy^{-\frac{1}{2}}\cdot y}$$

Accepted Answer

$$\frac{y^{\frac{5}{8}}}{y^2x}$$

Answer

$$\frac{y^{\frac{29}{8}}x^{\frac{3}{4}}}{x^3}$$

Answer

$$\frac{y^{\frac{5}{4}}x^{\frac{1}{3}}}{x^2}$$

Answer

$$\frac{x^{\frac{3}{4}}y^{\frac{25}{8}}}{x}$$

Question 12

Simplify. Your answer should contain only positive exponents with no rational exponents in the denominator.

$$\frac{x^{-\frac{3}{2}}y^{\frac{5}{3}}\cdot\left(x^2y^{-\frac{3}{2}}\right)^{-\frac{3}{2}}}{x^{-\frac{1}{3}}y^{-\frac{1}{4}}}$$

Accepted Answer

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

Answer

$$\frac{x^{\frac{3}{4}}y^{\frac{1}{4}}}{x^4y^2}$$

Answer

$$\frac{y^{\frac{1}{6}}x^{\frac{1}{12}}}{y^3x}$$

Answer

$$y^{\frac{11}{4}}x^{\frac{5}{2}}$$

Question 13

Simplify. Your answer should contain only positive exponents with no rational exponents in the denominator.

$$\left(\frac{x^{\frac{3}{4}}y^{-2}\cdot x^{\frac{1}{2}}y^{-\frac{3}{2}}}{y^{-2}}\right)^{-\frac{3}{2}}$$

Accepted Answer

$$\frac{y^{\frac{9}{4}}x^{\frac{1}{8}}}{x^2}$$

Answer

$$\frac{x^{\frac{7}{12}}y^{\frac{1}{3}}}{y^2}$$

Answer

$$\frac{x^{\frac{7}{12}}y^{\frac{5}{2}}}{x}$$

Answer

$$\frac{y^{\frac{7}{12}}x^{\frac{1}{4}}}{yx^2}$$

Rational Exponents

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