GRE Math : How to add exponents

Study concepts, example questions & explanations for GRE Math

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Example Questions

Example Question #1 : How To Add Exponents

Simplify:  y3x4(yx3 + y2x2 + y15 + x22)

Possible Answers:

y3x12 + y6x8 + y45x4 + y3x88

y3x12 + y6x8 + y45 + x88

2x4y4 + 7y15 + 7x22

y4x7 + y5x6 + y18x4 + y3x26

y3x12 + y12x8 + y24x4 + y3x23

Correct answer:

y4x7 + y5x6 + y18x4 + y3x26

Explanation:

When you multiply exponents, you add the common bases:

y4 x7 + y5x6 + y18x4 + y3x26

Example Question #1 : How To Add Exponents

Indicate whether Quantity A or Quantity B is greater, or if they are equal, or if there is not enough information given to determine the relationship. 

\dpi{100} \small n>0

Quantity A: \dpi{100} \small 16^{n+2}

Quantity B: \dpi{100} \small 2^{4}\times (8^{n+1})^{2}\div 4^{n}

Possible Answers:

Quantity B is greater. 

Quantity A is greater.

The quantities are equal. 

The relationship cannot be determined from the information given.

Correct answer:

Quantity B is greater. 

Explanation:

By using exponent rules, we can simplify Quantity B.  

\dpi{100} \small \dpi{100} \small 2^{4}\times (8^{n+1})^{2}\div 4^{n}

\dpi{100} \small \dpi{100} \small 2^{4}\times (8^{2n+2})\div 4^{n}

  \dpi{100} \small \dpi{100} \small 2^{4}\times 2^{3(2n+2)}\div 4^{n}

\dpi{100} \small \dpi{100} \small 2^{4}\times 2^{6n+6}\div 4^{n} 

\dpi{100} \small \dpi{100} \small 2^{6n+10}\div 4^{n}

\dpi{100} \small \dpi{100} \small 2^{6n+10}\div 2^{2n}

\dpi{100} \small 2^{4n+10}

Also, we can simplify Quantity A. 

\dpi{100} \small 16^{n+2}

\dpi{100} \small =2^{4(n+2)}

\dpi{100} \small =2^{4n+8}

Since n is positive, \dpi{100} \small 4n+10>4n+8

Example Question #4 : Exponential Operations

If , what is the value of ?

Possible Answers:

Correct answer:

Explanation:

Rewrite the term on the left as a product. Remember that negative exponents shift their position in a fraction (denominator to numerator).

The term on the right can be rewritten, as 27 is equal to 3 to the third power.

Exponent rules dictate that multiplying terms allows us to add their exponents, while one term raised to another allows us to multiply exponents.

We now know that the exponents must be equal, and can solve for .

 

Example Question #3 : How To Add Exponents

If , what is the value of ?

Possible Answers:

Correct answer:

Explanation:

Since the base is 5 for each term, we can say 2 + n =12.  Solve the equation for n by subtracting 2 from both sides to get n = 10.

Example Question #2 : How To Add Exponents

Simplify .

Possible Answers:

Correct answer:

Explanation:

Start by simplifying each individual term between the plus signs. We can add the exponents in  and  so each of those terms becomes . Then multiply the exponents in  so that term also becomes . Thus, we have simplified the expression to  which is .

Example Question #3 : How To Add Exponents

Simplify .

Possible Answers:

Correct answer:

Explanation:

First, simplify  by adding the exponents to get .

Then simplify  by multiplying the exponents to get .

This gives us . We cannot simplify any further.

Example Question #4 : How To Add Exponents

If , what is the value of 

Possible Answers:

Correct answer:

Explanation:

To attempt this problem, note that .

Now note that when multiplying numbers, if the base is the same, we may add the exponents:

This can in turn be written in terms of nine as follows (recall above)

Example Question #5 : How To Add Exponents

If , what is the value of 

Possible Answers:

Correct answer:

Explanation:

When dealing with exponenents, when multiplying two like bases together, add their exponents:

However, when an exponent appears outside of a parenthesis, or if the entire number itself is being raised by a power, multiply:

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