How do you distribute exponents

Explanation : In order to solve this problem, each of the answer choices needs to be simplified. Explanation : Step 1: Distribute the exponents in the numberator. Step 2: Represent the negative exponents in the demoninator. Step 3: Simplify by combining terms. Explanation : Use the power rule to distribute the exponent:.

Explanation : Step 1: Distribute the exponent through the terms in parentheses: Step 2: Use the division of exponents rule. Explanation : When a power applies to an exponent, it acts as a multiplier, so 2a becomes 4a and -b becomes -2b.

Explanation : When faced with a problem that has an exponent raised to another exponent, the powers are multiplied: then simplify:. Explanation : Solve each term separately. Explanation : is the correct answer because the order of operations were followed and the multiplication and power rules of exponents were obeyed.

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Simplify the expression:. If you've found an issue with this question, please let us know. With the help of the community we can continue to improve our educational resources. If Varsity Tutors takes action in response to an Infringement Notice, it will make a good faith attempt to contact the party that made such content available by means of the most recent email address, if any, provided by such party to Varsity Tutors.

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Report an Error. Explanation : When you have an exponent outside of parentheses, it means it is necessary to distribute it to all parts of whatever numbers or variables are inside the parentheses. Distribute the exponent 4 to both the 3 and the 4 inside the parentheses Now take 3 to the fourth power or 3 four times in the numerator and 4 to the fourth power or 4 four times in the denominator This fraction does not reduce so this is the final answer.

Explanation : An exponent outside of a parentheses needs to be distributed to all the numbers and variables in the parentheses. Explanation : An exponent outside of a parentheses means the entire quantity is being raised to that power. Recall that when like bases are being multiplied together their exponents are added. Here is the distributive law with powers. So that exponent distributing over multiplication and division.

But it would be illegal if we had 8 plus or minus 5 to the 3rd. That would not be 8 to the 3rd plus or minus 5 to the 3rd. If we look at 8- 5 to the 3rd, well what is that? Of course that is 3 to the 3rd, which is And those two are not equal. In other words, we get two different numerical answers. We can do some legal math with sums or differences of power.

First we need to go back to that most impressive pattern in the distributive law. Now this is very tricky, when we read this equation from left to right, we say that we are distributing P. When we read this equation from right to left, we say that we are factoring out P. So distributing and factoring out are two sides of the same coin. Is divisible by any lower power of that same base.

Thus, in the sum of a higher power and a lower power of the same base, the greatest common factor of the two terms is the lower power, and this can be factored out because a lower power is always a factor of a higher power. Well, first of all we know that 17 to the 30th has to be divisible by 17 to the 20th.

Image by Venomous Vector. We know one is a factor of the other. And so 17 to the 20th is the greatest common factor of these two terms. And of course 17 to the 20th, I can write that as 17 to the 20th times 1. I factor out 17 to the 20th and I get 17 to the 20th times parentheses 17 to the 10th plus 1.

And that is a factored out form of those powers. Obviously the powers here are too large to simplify any of these resultant terms, but if the two powers in the sum are closer sometimes such simplification is easy. So I will say, pause the video and see if you can simplify this. In fact 3 to the 28th is the greatest common factor of these two terms.