# Algebraic Expressions with Exponents on the ISEE

#### Upper Level

**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:*

*n ^{x}n^{y} = n^{(x + y)}*, for example: 3

^{7}x 3

^{2}= 3

^{9}

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

, for example: 3^{7} ÷ 3^{2} = 3^{5}

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

√*n* = *n*^{½}

*4. A n egative exponent reciprocates the number:*

**Solution:**

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.