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

Study concepts, example questions & explanations for SSAT Upper Level Math

varsity tutors app store varsity tutors android store

Example Questions

Example Question #14 : Expressions & Equations

Evaluate:

Possible Answers:

The expression is undefined.

Correct answer:

Explanation:

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

If \dpi{100} x=\sqrt{34} then

Possible Answers:

Correct answer:

Explanation:

\dpi{100} \sqrt{25}=5

\dpi{100} \sqrt{36}=6

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:

Possible Answers:

Correct answer:

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: 

Possible Answers:

Correct answer:

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:

Possible Answers:

Correct answer:

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:

Possible Answers:

Correct answer:

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: 

Possible Answers:

Correct answer:

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: 

Possible Answers:

Correct answer:

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:

Possible Answers:

Correct answer:

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 

Possible Answers:

Correct answer:

Explanation:

To solve , 6 should be divided by 3. The exponent will be equal to the exponent of the numerator minus the exponent of the denominator. This results in:

Learning Tools by Varsity Tutors