# ISEE Upper Level Math : Numbers and Operations

## Example Questions

### Example Question #1 : How To Divide Exponents

Simplify:

Explanation:

Based on the quotient rule for exponents, we know that for any non-zero number  and any integers  and ,

.

We also know that any non-zero number raised to the power of is .

### Example Question #2 : How To Divide Exponents

Simplify:

Explanation:

We know that any non-zero number raised to the power of is equal to

Now factor:

### Example Question #91 : Numbers And Operations

Evaluate:

The expression is undefined.

Explanation:

We know that any non-zero number raised to the power of is equal to .

### Example Question #92 : Numbers And Operations

Evaluate:

Explanation:

Based on the quotient rule for exponents, we know that, for any non-zero number  and any integers  and

.

### Example Question #93 : Numbers And Operations

Simplify:

Explanation:

When a fraction is raised to a power, the numerator and the denominator are both raised to that power:

The power rule says that in order to raise a power to a power, we need to multiply the exponents, i.e.

,

where and are real numbers.

### Example Question #94 : Numbers And Operations

Evaluate:

Explanation:

When a fraction is raised to a power, the numerator and the denominator are both raised to that power:

The power rule says that in order to raise a power to a power, we need to multiply the exponents, i.e.

.

### Example Question #95 : Numbers And Operations

Simplify:

Explanation:

The Negative Exponent Rule says .

### Example Question #96 : Numbers And Operations

Evaluate:

Assume variables are non-zero.

Explanation:

We know that any non-zero number raised to the power of is equal to .

### Example Question #97 : Numbers And Operations

Evaluate:

Explanation:

When a fraction is raised to a power, the numerator and the denominator are both raised to that power. In addition, the power rule says that in order to raise a power to a power, multiply the exponents, i.e.

.

### Example Question #98 : Numbers And Operations

What is the value of the expression ?