Start by distributing the exponents into their respective terms. Recall that when an exponent is raised to an exponent, you will need to multiply the exponents together.

Next, multiply like terms together. Recall that when you multiply numbers that have the same base, you will need to add the exponents together.

Since the question asks for the product, we will need to multiply the two terms.

Start by distributing the exponents into the proper terms. Recall that when an exponent is raised to another exponent, you will need to multiply the two exponents together.

Next, multiply like terms together. Recall that when you multiply numbers that have the same base but different exponents, you will need to add the exponents together.

Start by distributing the exponent for the second term. Recall that when an exponent is raised to another exponent, you will need to multiply the exponents.

Next, multiply like terms together. Recall that when you multiply terms with the same base but different exponents, you will need to add the exponents together.

Start by distributing the exponent in the numerator. Recall that when a exponent is raised to another exponent, you will need to multiply the exponents together.

Next, recall that when you divide numbers with the same base but different exponents, you will need to subtract the two exponents.

In order to make the negative exponent positive, put it in the denominator.

Simplify the following expression:

To simplify this expression, we need to distribute the 4x cubed term. This means that we will multiply each term within the parentheses by the 4x term. 

So, this...

Is the same as

Now, to multiply exponents, we need to recall a rule.

This means that when we are multiplying variables, we need to add the values of their exponents (if they are the same variable). 

In this case, all of our variables are x's, so we can combine them by adding the values of the exponents. 

For the coefficients (numbers out in front), all we have to do is multiply them as we  would any other number.

So, let's tackle our first step:

Now for the second step:

Let's put it all together to get:

Start by distributing the exponent in the numerator. Recall that when an exponent is raised to another exponent, you will need to multiply the exponents together.

Next, distribute the exponent in the denominator.

Now, rewrite the fraction with the exponents distributed properly.

Now simplify like terms. Recall that when two numbers with the same base but different exponents are found in a fraction, you will need to subtract the exponent in the denominator from the exponent in the numerator.

To make a negative exponent positive, put the term with the exponent in the denominator.

Simplify the following expression:

To combine these, we need to multiply the coefficients and add our exponents.

Simplify the following expression:

To simplify this, we need to divide our coefficients and subtract our exponents.

So, our answer is:

First, rewrite  as an improper fraction:

Substitute:

Multiply, taking  as a factor three times:

Multiply numerators, then multiply denominators: 

Rewrite as a mixed number by dividing 125 by 27.

, so

.

, the result of taking 5 as a factor three times:

2 raised to an integer power  is equal to 2 multiplied as a factor  times. So, for example, 

2 can be raised to the power of the other integers similarly, although, as can be seen, each consecutive power of 2 can be found by multiplying the previous power by 2:

We do not need to go further.  is the least integer value of the exponent  that yields a result greater than 125.