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Lesson 6.1 - Rational Exponents and nth Roots

Last updated over 1 year ago

8 questions

Note from the author:

Instructions

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I can define rational exponents and nth roots and use them to solve real-world problems.

I can define rational exponents and nth roots and use them to solve real-world problems.

Question 1

1.

Write the expression as an expression with a rational exponent.

Question 2

2.

Write the expression as an expression with a rational exponent.

Question 3

3.

Evaluate the following expression.

Question 4

4.

Evaluate the following expression.

Question 5

5.

Write the expression as a radical expression and simplify if possible.

Question 6

6.

Write the expression as a radical expression and simplify if possible.

Question 7

7.

Write an equivalent expression to
that has a different base and a different rational exponent.

Question 8

8.

The power function,

and

model two different data sets of trees. Each function can be used to estimate the biomass M (in kilograms) of a tree above ground, where d is the diameter (in centimeters) of the tree 4.5 feet above the ground. Biomass is the mass of all living things including the tree and anything living in the tree. Rewrite the functions using rational exponents. Then, determine how many times greater the biomass of a tree with a diameter of 20 centimeters from the data set of A is compared to a tree of the same diameter from data set B.