# ISEE Upper Level Math : Variables and Exponents

## Example Questions

Evaluate .

Explanation:

### Example Question #81 : Variables

Evaluate .

Explanation:

To solve for the variable isolate it on one side of the equation with all of constants on the other side.

First add one third to both sides.

Calculate a common denominator to add the two fractions.

Square both sides to solve for y.

### Example Question #83 : Variables

Simplify the following:

Explanation:

Simplify the following:

Let's recall the rules for distributing exponents.

We treat coefficients (like the 7) like regular numbers and raise them to the new exponent.

We deal with variables (like the t, h, and b) by multiplying their current exponent by the new exponent.

Doing so yields:

Simplify to get:

### Example Question #84 : Variables

Evaluate .

Explanation:

By the Power of a Power Principle,

So

Also, by the Power of a Product Principle,

, so, substituting,

.

### Example Question #85 : Variables

Evaluate .

Explanation:

By the Power of a Product Principle,

Also, by the Power of a Power Principle,

Combining these ideas, then substituting:

### Example Question #1 : How To Subtract Exponential Variables

Simplify the expression:

The expression cannot be simplified further.

Explanation:

Group, then collect like terms:

Simplify:

Explanation:

### Example Question #81 : Variables

Assume that . Which of the following expressions is equivalent to:

?

Explanation:

If , simplify:

Explanation:

If , simplify: