Question

complete the steps to simplify \\(\sqrt5{4} \cdot \sqrt{2}\\)
rewrite using rational exponents.
\\(2^{\frac{2}{5}} \cdot 2^{\frac{1}{2}}\\)
\\(4^5 \cdot 2^2\\)
\\(4^{\frac{1}{5}} \cdot 2^{\frac{1}{2}}\\)

what is the least common denominator of the exponents?
10

rewrite \\(\sqrt5{4} \cdot \sqrt{2}\\) as a single radical.
\\(\sqrt10{2^3}\\)
\\(\sqrt10{2^9}\\)
\\(\sqrt9{2^{10}}\\)

find the simplified product:
\\(\sqrt{2x^3} \cdot \sqrt{18x^5}\\)
\\(\sqrt{6x^4}\\)
\\(\sqrt{36x^8}\\)
\\(18x^4\\)

Explanation:

Rewrite using rational exponents

Using the Radical to Exponential Form and Rational Exponents knowledge points

$$
LATEXBLOCK0
$$

Find the least common denominator

Using the Least Common Denominator knowledge point

$$
LATEXBLOCK1
$$

Rewrite as a single radical

Using the Rational Exponents knowledge point

$$
LATEXBLOCK2
$$

Find the simplified product

Using the Product Property of Radicals and Simplifying Radical Products knowledge points

$$
LATEXBLOCK3
$$

Answer:

Question 1

• (A) \(2^{\frac{2}{5}} \cdot 2^{\frac{1}{2}}\) (Correct answer)
• (B) \(4^{\frac{2}{5}} \cdot 2^2\)
• (C) \(4^{\frac{1}{5}} \cdot 2^{\frac{1}{2}}\)

Question 2

The least common denominator of the exponents is <blank>10</blank>.

Question 3

• (A) \(\sqrt[10]{2^3}\)
• (B) \(\sqrt[10]{2^9}\) (Correct answer)
• (C) \(\sqrt[9]{2^{10}}\)

Question 4

• (A) \(\sqrt{6x^4}\)
• (B) \(\sqrt{36x^8}\)
• (C) \(18x^4\) (Correct answer)