Section P.4 Homework

1.Using exponential notation, we can write

as _____

2.  Explain how we rationalize a denominator.

Complete the following steps to rationalize 

3. Write the radical expression using exponents.

4.  Write the exponential expression using radicals. 

5.  Write the exponential expression using radicals.

6.  Write the radical expression using exponents.

7.  Evaluate each expression.

A.

B.

C.

8. Simplify the expression. Assume that x and y denote any real numbers.

$\sqrt{x^8}{y}^4$

9.  Simplify the expression

$\sqrt[3]{54}–\sqrt[3]{16}$

10.  Evaluate each expression.

A.

B.  

C.

11.  Evaluate the expression using x = 1, y = 2, and z = −1.

$\sqrt[3]{x^3+11y+15z}$

12.  Simplify the expression and eliminate any negative exponent(s). Assume that all letters denote positive numbers.

A.

B

13. Simplify the expression and eliminate any negative exponent(s). Assume that all letters denote positive numbers.

A.

B.

14. Simplify the expression and express the answer using a rational exponent. Assume that y denotes a positive number.

$\left(\sqrt[7]{y^6}\right)\left(\sqrt[4]{y^3}\right)$

15. Put each fractional expression into standard form by rationalizing the denominator.

A.

B. 

C.

16.

Because of the curvature of the earth, the maximum distance D that you can see from the top of a tall building of height h is estimated by the formula

$D=\sqrt{2rh+h^2}$

where r=3960 mi is the radius of the earth and D and h are also measured in miles. How far can you see from the observation deck of a tall building, 1195 ft above the ground? (Round your answer to one decimal place.)