# SAT Math : How to find patterns in exponents

## Example Questions

### Example Question #1231 : Psat Mathematics

Write in radical notation:

Possible Answers:

Correct answer:

Explanation:

Properties of Radicals

### Example Question #1232 : Psat Mathematics

Express in radical form :

Possible Answers:

Correct answer:

Explanation:

Properties of Radicals

### Example Question #1233 : Psat Mathematics

Simplify:

Possible Answers:

Correct answer:

Explanation:

### Example Question #1234 : Psat Mathematics

Simplify:

Possible Answers:

Correct answer:

Explanation:

Convert the given expression into a single radical e.g. the expression inside the radical is:

and the cube root of this is :

### Example Question #1235 : Psat Mathematics

Solve for .

Possible Answers:

Correct answer:

Explanation:

Hence  must be equal to 2.

### Example Question #1236 : Psat Mathematics

Simplify:

Possible Answers:

Correct answer:

Explanation:

Now

Hence the correct answer is

### Example Question #1237 : Psat Mathematics

Solve for .

Possible Answers:

Correct answer:

Explanation:

If we combine into a single logarithmic function we get:

Solving for  we get .

### Example Question #1238 : Psat Mathematics

If  is the complex number such that , evaluate the following expression:

Possible Answers:

Correct answer:

Explanation:

The powers of i form a sequence that repeats every four terms.

i= i

i2 = -1

i3 = -i

i4 = 1

i5 = i

Thus:

i25 = i

i23 = -i

i21 = i

i19= -i

Now we can evalulate the expression.

i25 - i23 + i21 - i19 + i17..... + i

= i + (-1)(-i) + i + (-1)(i) ..... + i

= i + i + i + i + ..... + i

Each term reduces to +i. Since there are 13 terms in the expression, the final result is 13i.

### Example Question #15 : Algebra

If , then which of the following must also be true?

Possible Answers:

Correct answer:

Explanation:

We know that the expression must be negative. Therefore one or all of the terms x7, y8 and z10 must be negative; however, even powers always produce positive numbers, so y8 and z10 will both be positive. Odd powers can produce both negative and positive numbers, depending on whether the base term is negative or positive. In this case, x7 must be negative, so x must be negative. Thus, the answer is x < 0.

### Example Question #17 : Algebra

Simplify the following:

Possible Answers:

Correct answer:

Explanation:

With problems like this, it is always best to break apart your values into their prime factors. Let's look at the numerator and the denominator separately:

Numerator

Continuing the simplification:

Now, these factors have in common a . Factor this out:

Denominator

This is much simpler:

Now, return to your fraction:

Cancel out the common factors of :