Simplify the following expression:

To solve this question, we need to recall that when dividing exponents we subtract them.

When dividing coefficients, we treat them as regular division.

In this case, we can break up our question into two parts:

The coefficients will simply reduce to "2", because 16 divided by 8 is two

The r's are another story. We subtract, so we will get the following:

So, if we put our two parts back together, we get:

Any nonzero number raised to the power of 0 is equal to 1, so . Therefore,

However, an expression with a denominator of 0 is undefined, so that is the correct choice.

Simplify the following:

Let's begin by recalling that when dividing variables with similar base, we need to subtract the exponents.

To deal with the coefficients, simply treat them as a fraction and simplify.

So our answer is

The Negative Exponent Rule says .

We know that any non-zero number raised to the power of is equal to .

Separate the fraction and apply the quotient of powers rule:

We know that any non-zero number raised to the power of is equal to .

First we need to subtract the numbers in parentheses. So we can write:

We can alternatively write:

Based on the negative exponent rule we have:

Which says negative exponents in the numerator get moved to the denominator and become positive exponents. And negative exponents in the denominator get moved to the numerator and become positive exponents. So we can write:

Based on the power rule for exponents we can write:

That means; to raise a power to a power we need to multiply the exponents.So we have:

Separate the equation:

When a fraction is raised to a power, the numerator and the denominator are both raised to that power. In addition, the power rule says that in order to raise a power to a power, multiply the exponents, i.e.

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