How to add exponents - GRE Quantitative Reasoning

When you multiply exponents, you add the common bases:

y4 x7 + y5x6 + y18x4 + y3x26

By using exponent rules, we can simplify Quantity B.

$2^{4}$times $(8^{n+1}$$)^{2}$div $4^{n}$

$2^{4}$times $(8^{2n+2}$)div $4^{n}$

$2^{4}$times $2^{3(2n+2)}$div $4^{n}$

$2^{4}$times $2^{6n+6}$div $4^{n}$

$2^{6n+10}$div $4^{n}$

$2^{6n+10}$div $2^{2n}$

$2^{4n+10}$

Also, we can simplify Quantity A.

$16^{n+2}$

$=2^{4(n+2)}$

$=2^{4n+8}$

Since n is positive, 4n+10>4n+8

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 .

First, simplify by adding the exponents to get .

Then simplify by multiplying the exponents to get .

This gives us . We cannot simplify any further.

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 .

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)

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:

When you multiply exponents, you add the common bases:

y4 x7 + y5x6 + y18x4 + y3x26

By using exponent rules, we can simplify Quantity B.

$2^{4}$times $(8^{n+1}$$)^{2}$div $4^{n}$

$2^{4}$times $(8^{2n+2}$)div $4^{n}$

$2^{4}$times $2^{3(2n+2)}$div $4^{n}$

$2^{4}$times $2^{6n+6}$div $4^{n}$

$2^{6n+10}$div $4^{n}$

$2^{6n+10}$div $2^{2n}$

$2^{4n+10}$

Also, we can simplify Quantity A.

$16^{n+2}$

$=2^{4(n+2)}$

$=2^{4n+8}$

Since n is positive, 4n+10>4n+8

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.

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 .

First, simplify by adding the exponents to get .

Then simplify by multiplying the exponents to get .

This gives us . We cannot simplify any further.

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 .

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)

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:

When you multiply exponents, you add the common bases:

y4 x7 + y5x6 + y18x4 + y3x26

By using exponent rules, we can simplify Quantity B.

$2^{4}$times $(8^{n+1}$$)^{2}$div $4^{n}$

$2^{4}$times $(8^{2n+2}$)div $4^{n}$

$2^{4}$times $2^{3(2n+2)}$div $4^{n}$

$2^{4}$times $2^{6n+6}$div $4^{n}$

$2^{6n+10}$div $4^{n}$

$2^{6n+10}$div $2^{2n}$

$2^{4n+10}$

Also, we can simplify Quantity A.

$16^{n+2}$

$=2^{4(n+2)}$

$=2^{4n+8}$

Since n is positive, 4n+10>4n+8

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.

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 .