In this exercise, make the given changes in the indicated examples of this section and then solve the given problems.

In Example $2(b)$, change the square root to a cube root and then evaluate.

In this exercise, make the given changes in the indicated examples of this section and then solve the resulting problems.

In Example $3$, change $12$ to $-12$ in each of the four illustrations and then solve.

In this exercise, make the given changes in the indicated examples of this section, and then solve the resulting problems.

In Example $5$(c), change $3$ to and then evaluate.

Determine each of the following as being either true or false.

The absolute value of any real number is positive.

In this exercise, make the given changes in the indicated examples of this section, and then answer the given questions.

In the first line of Example $1$, change the $5$ to $-3$ and the $-19$ to $14$. What other changes must then be made in the first paragraph?

Make the given changes in the indicated examples of this section, and then solve the resulting problems.
In Example $5$(c ), change $3$ to $1-22$ and then evaluate

In this exercise, make the given changes in the indicated examples of this section, and then solve the resulting problems.

In Example $2(b)$, change the factor $\left(-s t^4\right)^2$ to $\left(-s t^4\right)^3$.

In this exercise, make the given changes in the indicated examples of this section and then perform the indicated divisions.

In Example $1(c)$, change the denominator to $-2 a^2 x y^5$.

In this exercise, make the given changes in the indicated examples of this section, and then solve the resulting problems.

In Example $6(a)$, change $2x$ to $2y$.

In this exercise, solve for the given letter from the indicated example of this section.

For the formula in Example $2$, solve for $a$.

In this exercise, make the given changes in the indicated examples of this section, and then solve the resulting problems.

In Example $6(a)$, change $2x$ to $2y$.

The solution of the equation $b^{3}=8$ is called the cube root of 8. The idea is similar to that of the square root, except that the cube root of 8 must be cubed (multiplied by itself three times) to become 8. One way to write the cube root of 8 is using the notation $\sqrt[3]{8}$. How can this notation be used to write the solution of $t^{5}=11$?

(a) Prove that $\ln x = 3 - 2x$ has at least one real root.
(b) Use your calculator to find an interval of length $0.01$ that contains a root.

Perform the indicated operations and write each answer in the standard form a + bi.

(3 + square root of -4) + (2 - square root of -16)