# ISEE Upper Level Math : How to find the exponent of variables

## Example Questions

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### Example Question #1 : How To Find The Exponent Of Variables

Simplify:

Explanation:

Apply the power of a product property:

### Example Question #2 : How To Find The Exponent Of Variables

What is the coefficient of  in the expansion of .

Explanation:

By the Binomial Theorem, if  is expanded, the coefficient of  is

.

Substitute : The coefficient of  is:

### Example Question #1 : How To Find The Exponent Of Variables

Simplify the expression:

Explanation:

Apply the power of a power property twice:

### Example Question #961 : Isee Upper Level (Grades 9 12) Mathematics Achievement

What is the coefficient of  in the expansion of  ?

Explanation:

By the Binomial Theorem, the  term of  is

,

making the coefficient of

.

We can set  in this expression:

### Example Question #5 : How To Find The Exponent Of Variables

What is the coefficient of  in the expansion of  ?

Explanation:

By the Binomial Theorem, the  term of  is

.

Substitute  and this becomes

.

The coefficient is

.

### Example Question #2 : How To Find The Exponent Of Variables

Evaluate:

Explanation:

We need to apply the power of power rule twice:

### Example Question #1 : How To Find The Exponent Of Variables

Solve for .

Explanation:

Based on the power of a product rule we have:

The bases are the same, so we can write:

### Example Question #11 : Variables And Exponents

Simplify:

Explanation:

First, recognize that raising the fraction to a negative power is the same as raising the inverted fraction to a positive power.

Apply the exponent within the parentheses and simplify.

This fraction cannot be simplified further.

### Example Question #1 : How To Find The Exponent Of Variables

Simplify:

Explanation:

First, recognize that raising the fraction to a negative power is the same as raising the inverted fraction to a positive power.

Apply the exponent within the parentheses and simplify.

### Example Question #971 : Isee Upper Level (Grades 9 12) Mathematics Achievement

Simplify if and .