Question

make sure to enter all answers in exact form. decimal approximations will be marked incorrect
question 1

true or false.

a. all expressions of the form ( a^{\frac{1}{n}} ) represent irrational numbers.

b. when we enter an exponent ( \frac{1}{n} ) into a calculator, we should enclose it in parentheses.

c. in the expression ( 16x^{\frac{1}{4}} ), the exponent does not apply to 16.

d. you can use your calculator to find a decimal equivalent for an irrational number.

question help: message instructor

Explanation:

A. Consider $x=4$: $4^\frac{1}{2}=2$, which is rational, so the statement is false.
B. Calculators follow order of operations; $\frac{1}{n}$ as an exponent needs parentheses to avoid misinterpretation (e.g., $8^\frac{1}{3}$ vs $8^1/3$), so the statement is true.
C. In $16x^\frac{1}{4}$, exponent rules mean only $x$ is raised to $\frac{1}{4}$, not 16, so the statement is true.
D. Calculators can only give a decimal approximation of an irrational number (not the exact value), but they can produce a decimal equivalent approximation, so the statement is true.

Answer:

A. False
B. True
C. True
D. True