# ACT Math : How to add exponents

## Example Questions

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

If , what is the value of ?

Explanation:

Rewrite the term on the left as a product. Remember that negative exponents shift their position in a fraction (denominator to numerator).

The term on the right can be rewritten, as 27 is equal to 3 to the third power.

Exponent rules dictate that multiplying terms allows us to add their exponents, while one term raised to another allows us to multiply exponents.

We now know that the exponents must be equal, and can solve for .

### Example Question #11 : Exponential Operations

If , what is the value of ?

Explanation:

Since the base is 5 for each term, we can say 2 + n =12.  Solve the equation for n by subtracting 2 from both sides to get n = 10.

### Example Question #41 : Exponential Operations

Which expression is equivalent to the following?

None of these

None of these

Explanation:

The rule for adding exponents is . We can thus see that  and  are no more compatible for addition than  and  are.

You could combine the first two terms into , but note that PEMDAS prevents us from equating this to  (the exponent must solve before the distribution).

### Example Question #42 : Exponential Operations

Express as a power of 2:

The expression cannot be rephrased as a power of 2.

Explanation:

Since the problem requires us to finish in a power of 2, it's easiest to begin by reducing all terms to powers of 2. Fortunately, we do not need to use logarithms to do so here.

Thus,

### Example Question #43 : Exponential Operations

Simplify the following expression:

Explanation:

When multiplying bases that have exponents, simply add the exponents. Note that you can only add the exponents if the bases are the same. Thus:

### Example Question #51 : Exponential Operations

Simplify the following:

Explanation:

When multiplying two exponential expressions with the same bases, add the exponents. In this problem, the answer turns out to be .

### Example Question #52 : Exponential Operations

Simplify the following

.

Explanation:

Begin by performing the last group's multiplication:

Now, remember that you treat variables and their powers as similar terms to be combined. Therefore, you can combine the  and  terms, giving you:

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