### All ISEE Upper Level Quantitative Resources

## Example Questions

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

**Possible Answers:**

The expression is undefined.

**Correct answer:**

The expression is undefined.

The numerator is undefined, since 0 raised to the power of 0 is an undefined quantity. Therefore, the entire expression is undefined.

### Example Question #12 : Exponential Operations

Column A Column B

**Possible Answers:**

The quantity in Column B is greater.

The quantities are equal.

There is not enough information to determine the relationship between the quantities.

The quantity in Column A is greater.

**Correct answer:**

The quantity in Column B is greater.

Let's simplify both quantities first before we compare them. becomes because the fractional exponent indicates a square root. We can simplify that by knowing that we can take the square roots of both the numerator and denominator, as shown by: . We can simplify further by taking the square roots (they're perfect squares) and get . Then, let's simplify Column B. To get rid of the negative exponent, we put the numerical expression on the denominator. There's still the fractional exponent at play, so we'll have a square root as well. It looks like this now: . We already simplified , so we can just plug in our answer, , into the denominator. Since we don't want a fraction in the denominator, we can multiply by the reciprocal of , which is 4 to get , which is just 4. Therefore, Column B is greater.

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

Give the reciprocal of in scientific notation.

**Possible Answers:**

**Correct answer:**

The reciprocal of is the quotient of 1 and the number;

This is not in scientific notation, so adjust.

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

Give the reciprocal of in scientific notation.

**Possible Answers:**

**Correct answer:**

The reciprocal of is the quotient of 1 and the number, or

This is not in scientific notation, so adjust:

### Example Question #21 : Exponential Operations

Column A Column B

**Possible Answers:**

The quantity in Column A is greater.

The relationship between the columns cannot be determined.

The quantity in Column B is greater.

The quantities in both columns are equal.

**Correct answer:**

The quantity in Column A is greater.

You can simplify Column A first. When you're dividing with exponents and bases are the same, subtract the exponents. Therefore, it simplifies to x. We know that x is positive since it is greater than 1. X is greater than . Try plugging in a number to test. 25 is greater than , which is 5. Even 1.1 is greater than . Therefore, Column A is greater.

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