How to add exponents - ISEE Upper Level: Quantitative Reasoning

The sum of the first ten perfect square integers:

The sum of the first five perfect cube integers:

(A) is greater.

The perfect squares between 50 and 100 inclusive are

Their sum is

In order to add exponential terms, both the base and the exponent must be the same. So we can write:

Based on the zero-exponent rule we have:

That means any non-zero number raised to the zero power is equal to . So we can write:

When exponents are multiplied by one another, and the base is the same, the exponents can be added together.

The first step is to try to create a common base.

Given that the square of 2 is for, the expression can be rewritten as:

When values, having the same base, are multiplied by one another, the exponents are added together and the base stays the same.

Thus,

is equal to

When multiplying exponents, the exponents are added together. Thus, 3 and 7 are added together for a sum of 10. In this problem, the "2" becomes a coefficient in front of the x. Therefore, the correct answer is:

To simplify this problem we need to factor out a

We can do this because multiplying exponents is the same as adding them. Therefore,

When multiplying exponents, the exponents are added together.

When multiplying exponents, the exponents are added together.

It is not necessary to evaluate both terms and multiply.

According to the rules of exponents, when we have the same bases raised to some power that are multiplied with each other, we can add the powers.

This term can be rewritten as a fraction.

The answer is:

Based on the product rule for exponents in order to multiply two exponential terms with the same base, add their exponents:

So we can write:

When you are adding and subtracting terms with exponents, you combine like terms. Since both columns have expressions with the same exponent throughout, you are good to just look at the coefficients. Remember, a coefficient is the number in front of a variable. Therefore, Column A is since . Column B is since . We can see that Column B is greater.

The sum of the first ten perfect square integers:

The sum of the first five perfect cube integers:

(A) is greater.

The perfect squares between 50 and 100 inclusive are

Their sum is

In order to add exponential terms, both the base and the exponent must be the same. So we can write:

Based on the zero-exponent rule we have:

That means any non-zero number raised to the zero power is equal to . So we can write: