# EXPONENTS AND SQUARE ROOTS PRACTICE FOR SAT

Problem 1 :

If a-1/2 = 3, what is the value of a ?

a)  -9    b)  1/9     c)  1/3      d)  9

Solution :

a-1/2 = 3

Taking square on both sides.

(a-1/2)2 = 32

a-1 = 9

1/a = 9

a = 1/9

So, the value of a is 1/9.

Problem 2 :

Let n = 12  + 14 + 16 + 18 + ........ + 150

what is the value of n ?

a)  10     b)  20    c)  25      d)  30

Solution :

n = 12  + 14 + 16 + 18 + ........ + 150

= 2 + 4 + 6 + 8 + .......... + 50

= 2(1 + 2  + 3 +  ............ + 25)

From this, it is clear the sequence had 25 terms.

So, the sum of the given series is 25.

Problem 3 :

If 42n + 3 = 8n + 5

what is the value of n ?

a)  6     b)  7    c)  8      d)  9

Solution :

42n + 3 = 8n + 5

22(2n + 3)= 23(n + 5)

2(4n + 6)= 23n + 15

Equating the powers, we get

4n + 6 = 3n + 15

4n - 3n = 15 - 6

n = 9

Problem 4 :

If 2x/2y = 23, then x must equal

a)  y + 3     b)  y - 3      c)  3 - y       d)  3y

Solution :

2x/2y = 23

2x - y23

Bases are equal, then we can equate the powers.

x - y = 3

x = 3 + y

Problem 5 :

If 3x = 10, what is the value of 3x - 3 ?

a)  10/3     b)  10/9      c)  10/27       d)  27/10

Solution :

3x - 3 3x 3-3

= 3x /33

Applying the value of 3x, we get

= 10/27

So, option c is correct.

Problem 6 :

If x2 y3 = 10 and x3y2 = 8, what is the value of x5y5 ?

a)  18    b)  20      c)  40       d) 80

Solution :

x2 y3 = 10 ------(1)

x3y2 = 8  ------(2)

(1) ⋅ (2)

x2 y⋅ x3y2 = 10(8)

x2+3 y3+2 = 80

x5y= 80

Problem 7 :

If a and b are positive even integers, which of the following is greatest ?

a)  (-2a)b       b)  (-2a)2b       c)  (2a)b        d)  2a2b

Solution :

Since a and b are even integers, let us take an assumption.

a = 2 and b =4

 Option a := (-2a)b = (-2(2))4= (-4)4= 256 Option b := (-2a)2b= (-2(2))2(4)= (-4)8= 65536 Option c := (2a)b= [2(2)]4= 44= 256 Option d := 2a2b= 2(2)2(4)= 2(2)8= 512

So, option b is correct.

Problem 8 :

Which of the following is equivalent to x2a/b, for all values of x ?

Solution :

Problem 9 :

If x2 = y3, for what value of z does x3z = y9 ?

a)  -1       b)  0       c)  1        d)  2

Solution :

x2 = y3

Raise power 3 on both sides.

(x2)3 = (y3)3

x6 = y9

Comparing with x3z = y9

3z = 6

z = 6/3

z = 2

So, option d is correct.

Problem 10 :

If 2x+3 - 2x = k(2x), what is the value of k ?

a)  3       b)  5       c)  7        d)  8

Solution :

2x+3 - 2x = k(2x)

2⋅ 23 - 2x = k(2x)

Factoring 2x, we get

2(23 - 1) = k(2x)

7 = k

Problem 11 :

If

a)  1/2       b)  3/4       c)  1        d)  4/3

Solution :

So, a = 1/2.

Problem 12 :

2(√x + 2) = 3√2

If x > 0 in the equation above, what is the value of x ?

a)  2.5    b)  3    c)  3.5      d)  4

Solution :

2(√x + 2) = 3√2

Take square on both sides.

4(x + 2) = 9(2)

4x + 8 = 18

4x = 18 - 8

4x = 10

x = 10/4

x = 5/2

x = 2.5

So, the answer is option a.

Problem 13 :

If xac  ⋅ xbc x30, x > 1 and a + b = 5, what is the vale of c?

a)  3    b)  5    c)  6      d)  10

Solution :

xac  ⋅ xbc x30

x(ac + bc) = x30

Equating the powers, we get

ac + bc = 30

Factoring c, we get

c(a + b) = 30

c (5) = 30

c = 30/5

c = 6

Problem 14 :

If n3 = x and n4 = 20x, where n > 0, what is the value of x ?

Solution :

n3 = x  ----(1)

n4 = 20x ------(2)

(2) / (1)

n4 / n3 = 20x / x

n = 20

Applying the value of n in (1), we get

203 = x

x = 8000

Problem 15 :

If x8 y7 = 333 and x7y6 = 3, what is the value of xy ?

Solution :

x8 y7 = 333 -----(1)

x7y6 = 3 ------(2)

(1) / (2)

x8 y7x7y6 = 333/3

xy = 111

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