# SSAT Upper Level Math : How to find the properties of an exponent

## Example Questions

### Example Question #14 : Expressions & Equations

Evaluate:

The expression is undefined.

Explanation:

### Example Question #11 : How To Find The Properties Of An Exponent

If then

Explanation:

34 is between 25 and 36, thus its square root must be between the square roots of 25 and 36.  x must be a number between 5 and 6.

### Example Question #11 : How To Find The Properties Of An Exponent

Express the result in scientific notation:

Explanation:

Applying the power of a product property of exponents, then the power of a power property:

This is not in scientific notation, so we adjust it as follows, applying the product of powers property:

### Example Question #14 : How To Find The Properties Of An Exponent

Assume all variables to be nonzero.

Simplify:

Explanation:

Since any nonzero expression taken to the power of 0 is equal to 1,

Using the power of a product property of exponents, this becomes

### Example Question #15 : How To Find The Properties Of An Exponent

Express the result in scientific notation:

Explanation:

Apply the product of powers property:

Since this is not in scientific notation, adjust as follows:

### Example Question #16 : How To Find The Properties Of An Exponent

Express the result in scientific notation:

Explanation:

Rewriting the numeator and applying the quotient of powers property:

This is not in scientific notation, so we adjust it as follows, applying the product of powers property:

### Example Question #17 : How To Find The Properties Of An Exponent

Assume all variables to be nonzero.

Simplify:

Explanation:

Any expression raised to the first power is equal to that expression, and any expression raised to the power of 0 is equal to 1, so

### Example Question #18 : How To Find The Properties Of An Exponent

Assume all variables to be nonzero.

Simplify:

Explanation:

Any nonzero expression to the power of zero is equal to 1:

### Example Question #19 : How To Find The Properties Of An Exponent

Express the result in scientific notation:

Explanation:

Rewriting the numerator and applying the quotient of powers property:

Since this is not in scientific notation, adjust as follows:

### Example Question #11 : How To Find The Properties Of An Exponent

What is the value of