Quiz about IM2 - Rational Exponents & Radicals

Question 1

Which expression is equivalent to $$109^{\frac{6}{5}}$$ ?

Accepted Answer

$$\sqrt[5]{109^6}$$

Answer

$$109^{\frac{5}{6}}$$

Answer

$$\sqrt[12]{109^{10}}$$

Answer

$$\sqrt[6]{109^5}$$

Question 2

Which expression is equivalent to $$\sqrt[3]{8^2}$$ .

Accepted Answer

$$8^{\frac{2}{3}}$$

Answer

$$8^{\frac{3}{2}}$$

Answer

$$22.6$$

Answer

$$\sqrt[3]{2^8}$$

Question 3

Which expression is equivalent to $$\left(\sqrt[4]{5}\right)^7$$ ?

Accepted Answer

$$5^{\frac{7}{4}}$$

Answer

$$\sqrt[7]{5^4}$$

Answer

$$5^{\frac{4}{7}}$$

Answer

$$\left(\frac{5}{4}\right)^7$$

Question 4

Which expression is equivalent to $$x^{\frac{2}{3}}$$ ?

Accepted Answer

$$\sqrt[3]{x^2}$$

Answer

$$\sqrt[]{x^3}$$

Answer

$$\sqrt[3]{x}$$

Answer

$$\sqrt[]{x^{\frac{3}{2}}}$$

Question 5

Which expression is equivalent to $$p^{\frac{1}{4}}$$ ?

Accepted Answer

$$\sqrt[4]{p}$$

Answer

$$\sqrt[1]{p^4}$$

Answer

$$\sqrt[]{p^4}$$

Answer

$$\sqrt[4]{p^{\frac{1}{4}}}$$

Question 6

Which expression is equivalent to $$\sqrt[]{c^5}$$ ?

Accepted Answer

$$c^{\frac{5}{2}}$$

Answer

$$c^5$$

Answer

$$c^{\frac{1}{5}}$$

Answer

$$c^{\frac{2}{5}}$$

Question 7

Which expressions are equivalent to $$2187^{\frac{5}{7}}$$ ?

Check ALL that apply!

Accepted Answer

$$\left(3\cdot3\cdot3\cdot3\cdot3\cdot3\cdot3\right)^{\frac{5}{7}}$$

Accepted Answer

$$3^5$$

Accepted Answer

$$243$$

Answer

$$3^7$$

Question 8

Which expressions are equivalent to $$\sqrt[3]{343^4}$$ ?

Check ALL that apply!

Accepted Answer

$$7^4$$

Accepted Answer

$$343^{\frac{4}{3}}$$

Answer

$$\left(7\cdot7\cdot7\cdot7\right)^{\frac{4}{3}}$$

Answer

$$7^3$$

IM2 - Rational Exponents & Radicals