Simplify the following expression:

When multiplying exponents, we need to recall the rule. When we multiply exponents of like base together, we add the exponents. This is seperate from the numbers out in front (the 5 and the 8) those two numbers will be multiplied as normal.

We can sort of rearrange the expression to get the following:

Making our answer:

Simplify the following expression:

Recall that when dividing exponents of like base, we need to subtract the exponents to simplify.

For our integers, we can either treat them like regular division, or rewrite them as exponents:

So our answer becomes:

To solve this problem you must recall that you need to subtract the exponents. Subtracting the smaller from the larger. 

So:

From here you need to get the negative exponent to be positive by bringing it to the top. 

So:

Then simplify:

The bases of the exponents are common.  This means we can add the fractions.

The least common denominator is six.

This becomes the power of the exponent.

Break up the fraction in terms so that each can be reduced.

Since we do not know term , it can be rewritten in base two, and .

Rewrite this term as a replacement of , and multiply the power of the exponent in base two with the power of the exponent in base eight.

Simplify the terms.  A value to the power of one-half is the square root of that number.

The answer is:  

The exponents can be subtracted since the bases are alike.

Subtract the top and bottom exponents.

The exponent becomes .  Eliminate the negative by taking the reciprocal of the base with the positive power.

The answer is:  

Simplify the following expression:

To simplify this expression, we need to divide the constant terms and subtract the exponents. In other words, we treat the whole numbers out in front just like a regular division problem and we subtract the exponents above the x's.

To simplify this expression, I would start by rewriting the negative exponents as positive. To do so, you have to place the term in its opposite place (if it's in the denominator, it then goes in the numerator). When you do that, you get: . Now, simplify each term separately. 9 goes into both 9 and 18, so that can be simpified. To simplify the x and w's, remember that when multiplying and bases are the same, you add the exponents. Therefore, your answer is: .

Simplify the following expression:

Let's begin by simplifying the fraction on the left.

When dividing exponents, we need to subtract them. treat the integers like you would any fraction:

Next, simplify the multiplications step by adding the exponents and treating the integers like regular multiplication:

So our answer is:

Simplify the following expression

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

When we do this, we get the following.

To simplify this expression, look at each term separately. , , , and . Put those all together to get: .