# ISEE Upper Level Quantitative : Variables

## Example Questions

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### Example Question #2 : How To Divide Exponential Variables

Simplify:

Explanation:

Break the fraction up and apply the quotient of powers rule:

### Example Question #42 : Variables And Exponents

Simplify:

Explanation:

To simplify this expression, look at the like terms separately. First, simplify . This becomes . Then, deal with the . Since the bases are the same and you're dividing, you can subtract exponents. This gives you Since the exponent is positive, you put in the numerator. This gives you a final answer of .

### Example Question #43 : Variables And Exponents

is a negative number.

Which is the greater quantity?

(a) The reciprocal of

(b) The reciprocal of

(a) and (b) are equal

(a) is the greater quantity

(b) is the greater quantity

It is impossible to determine which is greater from the information given

(b) is the greater quantity

Explanation:

A negative number raised to an odd power is negative; a negative number raised to an even power is positive. It follows that  is negative and  is positive. Also, the reciprocal of a nonzero number assumes the same sign as the number itself, so the reciprocal of  is positive and that of  is negative. It follows that the reciprocal of  is the greater of the two.

Simplify: