ISEE Upper Level Math : Exponential Operations

Example Questions

← Previous 1 3 4 5 6 7

Example Question #1 : Exponents

Simplify:

Explanation:

In order to add or subtract exponential terms, both the base and the exponent must be the same. So we can write:

Example Question #2 : Exponents

Evaluate:

Explanation:

In order to add or subtract exponential terms, both the base and the exponent must be the same. So we can write:

Now they must be multiplied out before they can be added:

Example Question #3 : Exponents

Subtract and simplify:

Explanation:

Consider a vertical subtraction process:

Rewrite as the addition of the opposite of the second expression, as follows:

Example Question #4 : Exponents

Define an operation  as follows:

For all real numbers ,

Evaluate: .

Explanation:

, so

Example Question #5 : Exponents

Subtract and simplify:

The correct answer is not among the other responses.

Explanation:

Consider a vertical subtraction process:

Rewrite as the addition of the opposite of the second expression, as follows:

Example Question #6 : Exponents

Define an operation  as follows:

For all real numbers ,

Evaluate: .

Explanation:

Example Question #7 : Exponents

Define an operation  as follows:

For all real numbers ,

Evaluate:

Explanation:

Example Question #8 : Exponents

Define  as follows:

Evaluate .

Explanation:

Example Question #9 : Exponents

Simplify the expresseion:

Explanation:

Variable terms can be combined by adding and subtracting if and only of they are like - that is, if each exponent of each variable is the same. In the given expression, no two exponents are the same. The terms cannot be combined, and the expression is already simplified.

Example Question #1 : Exponential Operations

Define a function  as follows:

Evaluate .