# ISEE Upper Level Math : How to divide exponents

## Example Questions

### 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 ?

Explanation:

When dealing with dividing scientific notation, you can divide the like terms separately. First, divide 4.2 by 7.0. This yields 0.6. Then divide the 10s. because when you divide a term with the same base, you subtract exponents. This gives you a combined answer of . Since this is not in scientific notation, move the decimal over one place to the right so that it will be in the appropriate notation. This gives you .

### Example Question #11 : How To Divide Exponents

What is a simplified version of the expression below?

Explanation:

When exponents are divided, the exponent in the denominator is subtracted from the exponent in the numerator. Given that the exponent in the numerator is , and the exponent in the denominator is , the resulting exponent will be  because . Thus,  will be raised to an exponent of

Meanwhile,  will be divided by , resulting in

### Example Question #12 : How To Divide Exponents

What is the value of the expression below?