# SAT Math : How to find patterns in exponents

## Example Questions

### Example Question #1231 : Psat Mathematics

Write in radical notation:

Explanation:

### Example Question #1232 : Psat Mathematics

Express in radical form :

Explanation:

Simplify:

Explanation:

### Example Question #1234 : Psat Mathematics

Simplify:

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 .

Explanation:

Hence  must be equal to 2.

### Example Question #1236 : Psat Mathematics

Simplify:

Explanation:

Now

Hence the correct answer is

### Example Question #1237 : Psat Mathematics

Solve for .

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:

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?

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:

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: