The formula for geometric sequences is defined by:

The term represents the first term, while is the common ratio. The term represents the terms.

Substitute the known values.

To determine the seventh term, simply substitute into the expression.

The answer is:

To raise to the power of any positive integer, divide the integer by 4 and note the remainder. The correct power is given according to the table below.

, so can be determined by selecting the power of corresponding to remainder 1. The correct power is , so .

When the base isn't explicitly defined, the log is base 10. For our problem, the first term

is asking:

For the second term,

is asking:

So, our final answer is

In order to rewrite a radical as an exponent, the number in the radical that indicates the root, gets written as a fractional exponent. Distribute the exponent to both terms by multiplying it by the exponents of each term as shown below:

From this point simplify the exponents accordingly:

Change the base of the inner term or log to base ten.

According to the log property:

The log based ten and the ten to the power of will cancel, leaving just the power.

The answer is:

Subtract six from both sides.

Simplify both sides.

Cube both sides to eliminate the cube root.

Divide by three on both sides.

The answer is:

Find the least common denominator to these fractions.

Multiply both denominators together.

Convert the fractions using this denominator.

The answer is:

Change the base of the inner term or log to base ten.

According to the log property:

The log based ten and the ten to the power of will cancel, leaving just the power.

The answer is:

Below is the graph of :

The given graph is the graph of reflected in the -axis, then translated up 6 units. This graph is

, where .

The function graphed is therefore

When exponents with the same base are multiplied together, we we will simply add the exponents and keep the base the same.

Multiply: