Exponents

D. 64

First problems don't really have any tricks. Just apply the rules and the order of operations and you should get D

B) 2

If 2⁴= 4^x => 2⁴= 2 ^2x
2x=4 = >  x=2

B) 48
x² =64 
As often is the case, the easiest questions have an "easy" answer.

y³ =64
4³ =64

 

D. 7 ² As often is the case, the easiest questions have an "easy" answer.

This question is a test of order of operations and arithmetic

TRAP: Answer B  is the trap. Remember parentheses are first! Exponents second.

C. 3

To get this correct, you just have to know the rules of exponents explained at the top of this page.

3^x-2 =3  => 3^(3-2) =3

Errors on this question came, in all likelihood from misapplying the rules of exponents.

D. 24

To get this correct, you just have to know the rules of exponents explained at the top of this page.

m^x * m⁷=m²⁸=> (x+7)=28 => x=21
(m⁵)^y =m¹⁵=> 5y=15 => y=3
x+y=24

TRAP: Trying to figure out the value of m is a waste of time.

E. (3^a)^b-1 As often is the case, the most difficult questions have a "difficult" answer.

Think of the answer as follows

Let x= 3^a => (x ^b ) / x¹ =>x ^b-1

METHOD: SUBSTITUTE IN your own numbers for a and b and then compare to answer

 

TRAP: Answer A. 1^b is the trap you should come to always expect in the last problem of an SAT section.  This answer is just to simplistic for the 2^nd to last question.

C)3^(2+x)

METHOD: SUBSTITUTE IN your own values for x and y then see which answer choice works. To make your life easier, make x=2 and therefore y equals 9.  Now 9y=9*9=81. See which answer choice equals 81 which is C)

 

TEST TRAPS: There are many traps here and the way to avoid them as well as save valualbe test taking time is to use the SUBSTITUTE in method.

a^ba⁴=a^(b+4) = a¹²
b+4 =12
b=8

To get this correct, you need to be able to apply the exponent rules described at the top of this web page.

3.2 or 16/5

Not much to do beyond use the rules of exponents.

If you didn't get his correct, your error in all likelihood had something to do with the "+" sign. Remember that you can't combine the two left hand terms until you've simplified each to 3,000 + 200 which equals 3,200

Answer: 45
First, recognize that 27 is 3³
 27¹⁵ = (3³)¹⁵= 3^(3*15)= 3⁴⁵
3⁴⁵= 3 ^y

Not much to do beyond use the rules of exponents.