Exponents

Question 1

Exponents with a base of 0 always equal=?

Exponents with a base of 1 always equal=?

Answer 1

0. 0x0x0 =0

1. 1x1x1=1

Question 2

Any base to the power of 0 =?

Answer 2

1

Question 3

What happens to the value as an exponent increases and the base is a proper fraction?

Answer 3

The value gets smaller

Question 4

What is the rule about fractions raised to a power? (3/4)^2

Answer 4

You can distribute the exponent so (3/4)^2 becomes (3^2)/(4^2)= 9/16

Question 5

What is the rule about distribution of an exponent of a compound base? (2x5)^3

Answer 5

You can distribute the power to the bases. so 2^3 x 5^3

Question 6

What are the rules for negative bases?

Answer 6

If the negative is in parentheses then it distributes. When it is not in the parentheses then it is applied after the base^exponent is simplified.

(-2)^4= -2 x -2 x -2 x -2 =16
-2^4= -1 x 2 x 2 x 2 x 2 = -16

Question 7

How do you simplify exponential terms that have the same base and are being multiplied to each other? (2^6 x 2^21)

Answer 7

Add the exponents: 6+21= 27

2^27

Question 8

How do you simplify exponential terms that have the same base and are divided from each other? (2^21)/ (2^6)

Answer 8

Subtract the exponents: 21-6= 15

2^15

Question 9

How do you simplify negative exponents?

2^-2

Answer 9

Find the reciprical of the base and the exponent goes into the denominator: 2^-2= 1/(2^2)

Question 10

How do you simplify an exponential term that has two exponents? (2^3)^2

Answer 10

Multiply the exponents.

(2^3)^2= (2 x 2 x 2)(2 x 2 x 2)= 2^6
3x2=6

Question 11

What should you always do on the GMAT if you see exponential terms like this (11^3 +11^4)

Answer 11

Factor out a common factor.

11^3 ( 1 +11^1)= 11^3 (12)

Question 12

If the GMAT gives you a sq rt what is the possible value?

Answer 12

There is only one possible value, it would be positive. eg They give you “sq rt (4)” this would only equal 2.

Question 13

What are the possible values if the GMAT doesnt give you a sq rt but you take the sq rt of something ?

Answer 13

There will be two values; the positive and negative value. If you take “sq rt (4)” then you have to work with +2 and - 2.

Question 14

What does a fractional exponent mean and what order do you solve? 216^(1/3)

Answer 14

The denominator of the exponent is the root and the numerator of the exponent is the power. You can solve it in any order.

Question 15

What are the rules to simplifying roots with combo bases?

Answer 15

You can distribute the root if the bases are being multiplied or divided. But you cannot split the bases up if they are being added or subtracted.

Question 16

How do you find the roots of imperfect squares? eg sq rt(52)

Answer 16

Break the number down into its prime factors. Then take the primes that have multiples matched to the root out.
sq rt(52)
52= 2 x 2 x 13. 
= 2(sq rt(13))