### All PSAT Math Resources

## Example Questions

### Example Question #493 : Algebra

If and are nonzero numbers such that , which of the following is equivalent to ?

**Possible Answers:**

^{}

**Correct answer:**

For this problem, we need to make use of the property of exponents, which states that (x^{y})^{z} = x^{y}^{z}.

We are given a^{2} but are asked to find a^{6}.

Let's raise both sides of the equation to the third power, so that we will end up with a^{6} on the left side.

(a^{2})^{3} = (b^{3})^{3}

Now, according to the property of exponents mentioned before, we can multiply the exponents.

a^{(2*3)} = b^{(3*3)}

a^{6} = b^{9}

The answer is b^{9}.

### Example Question #492 : Algebra

If and are positive integers and , what is the value of ?

**Possible Answers:**

**Correct answer:**

The question tells us that 2^{2a} ( 2^{2b })= 16.

We can rewrite 16 as 2^{4}, giving us 2^{2a} ( 2^{2b })= 2^{4}.

When terms with the same base are multipled, their exponents can be added:

2^{(2a +2b) }= 2^{4}

Since the base is the same on both sides of the equation, we can equate the exponents:

2*a *+2*b *= 4

2(a + b) = 4

a + b = 2

### Example Question #21 : How To Multiply Exponents

Simplify:

**Possible Answers:**

**Correct answer:**

Apply the the various properties of exponents:

### Example Question #51 : Exponents

**Possible Answers:**

**Correct answer:**

### Example Question #61 : Exponents

Simplify:

**Possible Answers:**

This expression cannot be simplified any further

**Correct answer:**

When you are multiplying and the bases are the same, you add the exponents together. Because both bases are you add as your new exponent. You then keep the same base, , to the 7th power.

### Example Question #61 : Exponents

Solve for :

**Possible Answers:**

**Correct answer:**

Now the left side equals and the right side equals 8. Hence:

Therefore must be equal to 11.

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