Quiz about Lesson 7-3 Roots Review + Intro to Fraction Exponents

Question 1

We have established that exponents can be ADDED for product of powers,

such as $$9^2\cdot9^3=9^5$$ .

Based on this principle, what should $$9^{\frac{1}{2}}\cdot9^{\frac{1}{2}}$$ be equal to? Select TWO choices.

Accepted Answer

$$9^1$$

Accepted Answer

$$9$$

Answer

$$9^{\frac{1}{4}}$$

Answer

$$9^2$$

Question 2

We have established that exponents can be ADDED for product of powers, such as $$5^2\cdot5^4=5^6$$ .

Based on this principle, evaluate $$25^{\frac{1}{2}}\cdot25^{\frac{1}{2}}$$ . There are TWO correct re.

Accepted Answer

$$9^1$$

Accepted Answer

$$9$$

Answer

$$9^{\frac{1}{4}}$$

Answer

$$9^2$$

Question 3

We have established that exponents can be ADDED for product of powers,

such as $$9^2\cdot9^3=9^5$$ .

Based on this principle, $$2^{\frac{1}{3}}\cdot2^{\frac{1}{3}}\cdot2^{\frac{1}{3}}$$ is equal to -- (select TWO correct responses)

Accepted Answer

$$2^1$$

Accepted Answer

$$2$$

Answer

$$2^{\frac{1}{9}}$$

Answer

$$2^3$$

Question 4

Think this through: $$\sqrt[]{9}\cdot\sqrt[]{9}=9$$ because $$3\cdot3=9$$ .

We established that $$9^{\frac{1}{2}}\cdot9^{\frac{1}{2}}=9$$ , therefore, $$9^{\frac{1}{2}}$$ must equal -- (select TWO choices)

Accepted Answer

$$3$$

Accepted Answer

$$\sqrt[]{9}$$

Answer

$$9$$

Answer

$$\sqrt[]{3}$$

Question 5

We have seen that $$9^{\frac{1}{2}}=\sqrt[]{9}=3$$ .

Therefore, the fraction exponent 1/2 means the same thing as square root.

Which TWO of the following choices are equivalent to $$25^{\frac{1}{2}}$$ ?

Accepted Answer

$$5$$

Accepted Answer

$$\sqrt[]{25}$$

Answer

$$25$$

Answer

$$\sqrt[]{5}$$

Answer

$$\frac{25}{2}$$

Question 6

We have established that $$9^{\frac{1}{2}}=\sqrt[]{9}=3$$ .

Therefore, the fraction exponent 1/2 means the same thing as square root.

Which TWO of the following choices are equivalent to $$144^{\frac{1}{2}}$$ ?

Accepted Answer

$$12$$

Accepted Answer

$$\sqrt[]{144}$$

Answer

$$\sqrt[]{12}$$

Answer

$$12^2$$

Answer

$$\frac{144}{2}$$

Lesson 7-3 Roots Review + Intro to Fraction Exponents