How to multiply exponential variables

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ISEE Upper Level Quantitative Reasoning › How to multiply exponential variables

Questions 1 - 10
1

Multiply:

Explanation

This can be achieved by using the pattern of difference of squares:

Applying the binomial square pattern:

2

Simplify:

Explanation

First, simplify all of the exponents. When the exponent is outside of the parantheses, multiply it by the exponents inside so that you get: . Multiply so that you get 27. Then, multiply like terms. First, multilpy 2 by 27 so that you get 54. Then, multiply the x terms. Remember, when bases are the same, add the exponents: . Then, multiply the y terms: . Then, multiply all of the terms together so that you get .

3

Simplify the following:

None of the other answers

Explanation

To multiply variables with exponents, add the exponents. With multiple variables, simply add the exponents for each different variable.

Simplified:

4

Factor completely:

Explanation

The greatest common factor of the terms in is , so factor that out:

Since all factors here are linear, this is the complete factorization.

5

Simplify:

Explanation

6

Simplify the following:

None of the other answers

Explanation

To multiply variables with exponents, add the exponents. When there are constants mixed in, multiply the constants separately and put back in the final result:

7

Fill in the box to form a perfect square trinomial:

Explanation

To obtain the constant term of a perfect square trinomial, divide the linear coefficient, which here is 20, by 2, and square the quotient. The result is

8

Simplify the following expression:

Explanation

Simplify the following expression:

To combine these, we need to multiply our coefficients and our variables.

First, multiply the coefficients

Next, multiply our variables by adding the exponent:

So, we put it all together to get:

9

Solve the following:

Explanation

To multiply like variable with exponents, we will use the following formula:

Also, we will multiply coefficients like normal.

So, we get

10

Multiply the following:

Explanation

To multiply like variables with exponents, we will use the following formula:

So, we get

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