### All ACT Math Resources

## Example Questions

### Example Question #6 : How To Add Exponents

Simplify: h^{n} + h^{–2n }

**Possible Answers:**

^{}

^{}

^{}

**Correct answer:**

^{}

h^{–2n }= 1/h^{2n}

h^{n} + h^{–2n }= h^{n} + 1/h^{2n}

### Example Question #7 : How To Add Exponents

Simplify: 3y^{2} + 7y^{2} + 9y^{3} – y^{3} + y

**Possible Answers:**

10y^{2} + 8y^{3} + y

10y^{2} + 10y^{3} + y

10y^{4} + 8y^{6} + y

19y^{11}

10y^{2} + 9y^{3}

**Correct answer:**

10y^{2} + 8y^{3} + y

Add the coefficients of similar variables (y, y^{2}, 9y^{3})

3y^{2} + 7y^{2} + 9y^{3} – y^{3} + y =

(3 + 7)y^{2} + (9 – 1)y^{3} + y =

10y^{2} + 8y^{3} + y

### Example Question #8 : How To Add Exponents

Simplify the following:

**Possible Answers:**

**Correct answer:**

When common variables have exponents that are multiplied, their exponents are added. So *K*^{3 }* *K*^{4} =*K*^{(}^{3+4)} = *K*^{7}. And *M*^{6} * *M*^{2} = *M*^{(6+2)} = *M*^{8}. So the answer is *K*^{7}/*M*^{8}.

### Example Question #9 : How To Add Exponents

Solve for :

**Possible Answers:**

**Correct answer:**

First, reduce all values to a common base using properties of exponents.

Plugging back into the equation-

Using the formula

We can reduce our equation to

So,

### Example Question #84 : Exponents

Simplify: y^{3}x^{4}(yx^{3} + y^{2}x^{2} + y^{15} + x^{22})

**Possible Answers:**

y^{4}x^{7} + y^{5}x^{6} + y^{18}x^{4} + y^{3}x^{26}

y^{3}x^{12} + y^{6}x^{8} + y^{45} + x^{88}

2x^{4}y^{4} + 7y^{15} + 7x^{22}

y^{3}x^{12} + y^{6}x^{8} + y^{45}x^{4} + y^{3}x^{88}

y^{3}x^{12} + y^{12}x^{8} + y^{24}x^{4} + y^{3}x^{23}

**Correct answer:**

y^{4}x^{7} + y^{5}x^{6} + y^{18}x^{4} + y^{3}x^{26}

When you multiply exponents, you add the common bases:

y^{4} x^{7} + y^{5}x^{6} + y^{18}x^{4} + y^{3}x^{26}

### Example Question #85 : Exponents

If , what is the value of ?

**Possible Answers:**

**Correct answer:**

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 #86 : Exponents

If , what is the value of ?

**Possible Answers:**

**Correct answer:**

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?

**Possible Answers:**

None of these

**Correct answer:**

None of these

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:

**Possible Answers:**

The expression cannot be rephrased as a power of 2.

**Correct answer:**

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:

**Possible Answers:**

**Correct answer:**

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:

Certified Tutor