SAT Math : How to multiply exponents

Study concepts, example questions & explanations for SAT Math

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Example Questions

Example Question #61 : Exponential Operations

Simplify:

Possible Answers:

Correct answer:

Explanation:

When multiplying exponents, we just add the exponents while keeping the base the same.

Example Question #62 : Exponential Operations

Simplify:

Possible Answers:

Correct answer:

Explanation:

When multiplying exponents with different bases but the same exponent, you multiply the bases and keep the exponents the same.

Example Question #63 : Exponents

Define an operation  on the set of real numbers as follows:

For all real ,

Evaluate 

Possible Answers:

The value of  is an undefined quantity.

Correct answer:

Explanation:

Set  and  in the expression in the definition, then simplify the exponent:

Any nonzero number raised to the power of 0 is equal to 1, so 

.

Example Question #63 : Exponential Operations

Define an operation  on the set of real numbers as follows:

For all real ,

Evaluate: 

Possible Answers:

Correct answer:

Explanation:

Set  and  in the expression in the definition:

The exponent  simplifies as follows:

, so

Example Question #62 : Exponents

Convert the product of  to base .

Possible Answers:

Correct answer:

Explanation:

Although they have different bases, we know that .

Therefore 

.

Remember to apply the power rule of exponents.

Finally, 

.

Example Question #61 : How To Multiply Exponents

Solve for :

 

Possible Answers:

Correct answer:

Explanation:

 

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

Therefore  must be equal to 11.

Example Question #63 : Exponents

Define an operation  on the set of real numbers as follows:

For all real ,

Evaluate: .

Possible Answers:

The value of  is undefined.

Correct answer:

Explanation:

Set  and  in the expression in the definition, then simplify:

By definition, 

;

setting 

.

Substituting  and ,

Also, raising a number to the power of  is equivalent to taking the th root of the number; specifically, raising a number to the power of  is equivalent to taking its square root. Therefore, 

.

Example Question #472 : Algebra

Express  in terms of .

Possible Answers:

Correct answer:

Explanation:

By definition, 

and 

.

By the Power of a Power Rule, 

,

so, by substituting, 

.

Example Question #64 : Exponential Operations

Simplify the expression. 

Possible Answers:

Correct answer:

Explanation:

When multiplying with exponents, you must add the exponents.

Therefore, multiply the coefficients on the x terms and add the exponents

Example Question #61 : Exponents

Which of the following is equivalent to 

Possible Answers:

Correct answer:

Explanation:

 and  can be multiplied together to give you  which is the first part of our answer. When you multiply exponents with the same base (in this case, ), you add the exponents. In this case,  should give us  because . The answer is 

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