Algebraic Expressions with Exponents on the ISEE

Upper Level

LESSON GOAL: Learn to multiply and divide algebraic expressions with exponents on the ISEE.

ISEE Question:

Simplify the expression:

Normally, for a question with variables on the ISEE, the fastest solution is to plug in a number. Since we’re working with big exponents, however, the only reasonable number to plug in is 1 (even 2 would create extremely big results). 1 raised to any power is always 1, so the entire expression would equal 1, but unfortunately, so would the answer choices. This is a rare instance where plugging in doesn’t work.

Let’s review the basic rules for exponents:

1. When multiplying the same base, add the exponents:

nxny = n(x + y), for example: 37 x 32 = 39

2. When dividing the same base, subtract the exponents:

, for example: 37 ÷ 32 = 35

3. A square root is the same as an exponent of 1/2:

n = n½

4. A negative exponent reciprocates the number:


STEP 1: Simplify the square root (rule #3 above).

STEP 2: Flip the variables with negative exponents from numerator to denominator and vice versa to make them positive (rule #4).

STEP 3: Add the exponents in the numerator, then in the denominator (rule #1).

STEP 4: Simplify the fraction by subtracting the exponents (rule #2).

a−10 is not in the answer choices, but according to rule #4, we can reciprocate it to answer choice C)

Helpful Tip: All this being said, this problem is both challenging and time-consuming, so it’s a good one to skip, at least until you have given all other problems on this ISEE section a fair shot.