Free Printable INDICES QUIZ

1.

3²x 3⁵

a)

3⁶

b)

3⁷

c)

3⁸

d)

3¹⁰

2.

2b⁶ x 2b¹³

a)

2b¹⁹

b)

2b⁹

c)

4b¹⁹

d)

4b¹²

3.

q⁶ x q ^-6

a)

0

b)

q²

c)

q¹²

d)

1

4.

Simplify the following
3²x 2⁵x 3⁶x 2⁸

a)

3⁸x 2¹²

b)

3¹² x 2⁸

c)

3⁸x 2¹³

d)

2⁸x 3 ¹²

5.

Find the value
3x 4²x 3²

a)

3³x 4²

b)

4³x 3²

c)

434

d)

432

6.

2⁵÷ 2²

a)

1

b)

2³

c)

2⁷

d)

2¹²

7.

a⁵÷ a⁵

a)

a¹

b)

a⁵

c)

1

d)

a

8.

6a⁵÷ 2a²

a)

3a³

b)

12a³

c)

4a¹⁰

d)

2a⁷

9.

2m⁵n³÷ 3m²n

a)

2/3 m⁵n²

b)

2/3 m³n²

c)

6 m³n²

d)

2/3 m²n3

10.

36a⁸b⁷÷ 30ab³

a)

5/6 a⁸b⁴

b)

6/5 a⁷b³

c)

6/5 a³b⁷

d)

5/6 a⁷b³

11.

Simplify
3s⁴x 2t²x s³

a)

5st¹⁴

b)

5s⁷t²

c)

12 s⁷t ²

d)

6 s⁷t²

12.

Simplify $\left(x^2y\right)^3$

a)

$x^2y^3$

b)

$x^6y^3$

c)

$x^5y^3$

d)

$x^6y$

13.

Choose the equivalent values of $2^4$ .

a)

$4^2$

b)

16

c)

8

d)

$2\times2\times2\times2$

14.

Simplify 4⁰

a)

1

b)

4

c)

0

15.

$7^3$

What is the power?

a)

7

b)

3

16.

$5^2$

What is the Base?

a)

5

b)

2

17.

what is 2 x 2 x 2 x 2 x 2 x 2 x 2, written in index form?

a)

$2$

b)

$2^7$

c)

$7^2$

d)

128

18.

$3^{3\ }\times3^{7\ }\ =$

What is the answer in index form?

a)

$3^{21}$

b)

$9^{21}$

c)

$3^{10}$

d)

$9^{10}$

19.

$\left(3r^5s^3\right)^2\ =$

a)

$3r^7s^5$

b)

$9r^{10}s^6$

c)

$9r^7s^5$

d)

$3r^{10}s^6$

20.

Solve $4^{a-1}=8^{a+3}$ .

a)

$a=-11$

b)

$a=-4$

c)

$a=4$

d)

$a=11$

21.

Solve $25^{x+2}=\frac{1}{3125^x}$ .

a)

$x=\frac{4}{7}$

b)

$x=-\frac{4}{7}$

c)

$x=-\frac{7}{4}$

d)

$x=\frac{7}{4}$

22.

Solve $4^{a-1}=8^{a+3}$ .

a)

$a=-11$

b)

$a=-4$

c)

$a=4$

d)

$a=11$

23.

Solve $3^{a-2}\times27^a=\frac{1}{81}$ .

a)

$a=-2$

b)

$a=\frac{1}{2}$

c)

$a=2$

d)

$a=-\frac{1}{2}$

24.

Solve $25^{x+2}=\frac{1}{625^x}$ .

a)

$x=-\frac{2}{3}$

b)

$x=\frac{2}{3}$

c)

$x=-\frac{3}{2}$

d)

$x=\frac{3}{2}$

25.

Solve $4^{2x-1}=64^x$ .

a)

$x=1$

b)

$x=-1$

c)

$x=-\frac{1}{4}$

d)

$x=\frac{1}{4}$

26.

Solve $3^{a+3}-3^{a+2}=2\ \ \$ .

a)

$a=-2$

b)

$a=\frac{1}{2}$

c)

$a=2$

d)

No solution

27.

Solve $32^{4x}=4^{8x+6}$ .

a)

$x=3$

b)

$x=-3$

c)

$x=-\frac{1}{3}$

d)

$x=\frac{1}{3}$

28.

How else can you write $\sqrt{x}$ ?

a)

$x^{\frac{1}{2}}$

b)

$x^2$

c)

$x^{-2}$

d)

$x^{\frac{1}{4}}$

29.

64^⅓=

a)

4

b)

8

c)

6

d)

21.3

30.

Evaluate

a)

3

b)

18

c)

9

d)

6

31.

4^-½=

a)

2

b)

-2

c)

½

d)

-½

32.

Write the product using exponents:

(-2) ⋅ (-2) ⋅ (-2) ⋅ (-2) ⋅ (-2)

a)

-2⁵

b)

2^-5

c)

(-2)⁵

d)

(-2)^-5

33.

Which of the following is equivalent to the expression $\frac{1}{2x^7}$ ?

a)

$\left(2x\right)^{-7}$

b)

$\frac{1}{2}x^7$

c)

$\frac{1}{2}x^{-7}$

d)

$2x^{-7}$

34.

a)

t²⁴

b)

t¹²

c)

t¹⁸

d)

t^-12

35.

a)

b)

c)

d)

36.

$^n\sqrt{a^m}$ or $\left(^n\sqrt{a}\right)^m$ is equal to ...

a)

$a^{\frac{m}{n}}$

b)

$a^{\frac{n}{m}}$

c)

$\frac{a^m}{a^n}$

d)

$\frac{a^n}{a^m}$

37.

Which expression below is equivalent to $3x^5+5\sqrt{x}-\frac{7}{x^3}$ ?

a)

$3x^5-5x^2-7x^{-3}$

b)

$3x^5-5x^2+7x^3$

c)

$3x^5+5x^{-2}-7x^{-3}$

d)

$3x^5+5x^{\frac{1}{2}}-7x^{-3}$

38.

Simplify the following $3x^7\times2\sqrt{x}\times\frac{5}{x^3}$

a)

$30x^2$

b)

$30x^{\frac{21}{2}}$

c)

$30x^{\frac{9}{2}}$

d)

$30x^{\frac{7}{2}}$

39.

Which of the following is equivalent to this expression $2x^3\times4\sqrt{x^3}\times\frac{5}{2x^5}$ ?

a)

$20x^{-\frac{1}{2}}$

b)

$80x^2$

c)

$80x^{-\frac{1}{2}}$

d)

none of the above

40.

$Simplify\ \left(\sqrt{t}\right)^3\times\left(^5\sqrt{t}\right)^2$

a)

$t^{\frac{10}{9}}$

b)

$t^{\frac{19}{10}}$

c)

$t^9$

d)

$t^{\frac{9}{10}}$

41.

Express $\left(\sqrt{125}\right)^3$ in positive index form

a)

$\left(\frac{1}{125}\right)^{\frac{2}{3}}$

b)

$\left(\frac{1}{125}\right)^{\frac{3}{2}}$

c)

$125^{\frac{2}{3}}$

d)

$125^{\frac{3}{2}}$

42.

Express $\left(\frac{2}{3}\right)^{-5}$ in positive index form.

a)

$\left(\frac{3}{2}\right)^5$

b)

$\frac{1}{\left(\frac{2}{3}\right)^5}$

c)

$\left(\frac{1}{2}\right)^5$

d)

$\left(\frac{1}{3}\right)^5$

43.

Express $\frac{x^2}{6y^3}$ in negative index form.

a)

$\frac{6y^{-3}}{x^{-2}}$

b)

$6x^2y^{-3}$

c)

$\frac{y^{-3}}{6x^{-2}}$

d)

$\frac{x^2y^{-3}}{6}$

44.

$\left(6a^8b\right)\left(10a^3b^4\right)$

a)

$60a^5b^{-3}$

b)

$60a^{24}b^4$

c)

$16a^{11}b^5$

d)

$60a^{11}b^5$

45.

Simplify
3s⁴x 2t²x s³

a)

5st¹⁴

b)

5s⁷t²

c)

12 s⁷t ²

d)

6 s⁷t²

46.

Simplify (34x⁵y⁶z^-7)⁰

a)

34x⁵y⁶ / z⁷

b)

34x⁵y⁶ / x^-7

c)

0

d)

1

47.

Which expression is equivalent to the following?

a)

32x³y⁴

b)

32x⁹y¹³

c)

16x⁸y¹²

d)

16x⁶y⁷

48.

Find a^-80 ÷ a⁸

a)

a^-88

b)

a¹⁰

c)

a⁸⁸

d)

a^-72

49.

36a⁸b⁷÷ (30ab⁴)

a)

5/6 a⁸b⁴

b)

6/5 a⁷b³

c)

6/5 a³b⁷

d)

5/6 a⁷b³

50.

a)

-10

b)

0.04

c)

10

d)

25

51.

a)

1/9

b)

9

c)

1/81

d)

81

52.

The number below, when written in standard form is:

0.000\ 000\ 017\ 3

a)

$1.73\ \times10^{-8}$

b)

$1.73\ \times10^8$

c)

$17.3\ \times10^{-9}$

d)

$1.73\times10^{-9}$

53.

Calculate

(6 × 10²) + (3 × 10³)

Give your answer in standard form.

a)

3.6 × 10²

b)

3.6 × 10³

c)

3,600

54.

Write in standard form
6 x 10¹² ÷ (3 x 10⁴)

a)

18 x 10⁸

b)

2 x 10³

c)

2 x 10¹⁶

d)

2 x 10⁸

55.

Find the standard form value of (2.5 x $10^4$ ) x ( 6 x $10^{-9}$ )

a)

$15\ \times10^{-5}$

b)

$15\ \times10^{-4}$

c)

$1.5\ \times\ 10^{-4}$

d)

$1.5\ \times\ 10^{-6}$

56.

The rectangular floor of a living room measures 4000cm long and 2800cm wide. The floor is covered with square tiles each of side 20cm. Calculate the number of square tiles used to cover the floor of the living room.

a)

2.8 x 10⁴

b)

2.8 x 10⁸

c)

5.6 x 10⁴

d)

5.6 x 10⁸

57.

The number below, when written is standard form is:

21\ 600\ 000

a)

$216\ \times10^5$

b)

$21.6\ \times10^6$

c)

$2.16\ \times10^7$

d)

$2.16\times10^{-7}$

58.

Express the number below in standard form, correct to 3 significant figures:

0.7209

a)

$7.21\ \times10^{-1}$

b)

$7.20\times10^{-1}$

c)

$7.2\times10^{-1}$

d)

$7.21\times10$

59.

Express the number below in ordinary form:

5.23\times10^4

(a)

60.

The number 67 900 000 written in standard form, is

6.79\ \times10^n

. What is the value of "n" ?

(a)

61.

The number 0.000 000 000 067 written in standard form is

6.7\ \times10^n

. What is the value of "n"?

(a)

62.

Evaluate the following, expressing your answers in standard form,

3.2\ \times10^{-3\ }+\ 9.1\times10^{-4}\

a)

$4.11\times10^{-3}$

b)

$4.11^{-3}$

c)

$4.11\times10^3$

d)

$12.3\times10^{-7}$

63.

2.5 x 10²+ 1.35 x 10⁴ =

a)

1.375 x 10⁴

b)

3.85 x 10⁶

c)

1375

64.

Which of the following is in standard form?

a)

20.35 x 10⁴

b)

.2035 x 10⁴

c)

2035⁴

d)

2.035 x10⁴

65.

When writing a number in standard form, the first number must be greater than 1 but less than 10.

a)

FALSE

b)

TRUE

66.

When writing a number in standard form, the first number must be greater than OR equals to 1 but less than 10.

a)

FALSE

b)

TRUE

67.

Solve .
$2^{2x+3}=128$

a)

-2

b)

$-\frac{3}{2}$

c)

$\frac{3}{2}$

d)

2

68.

$3_{ }^{3x+1}=3^{x+3}$

Solve.

a)

4

b)

3

c)

2

d)

1

69.

Solve.
$\sqrt{3^x}=9$

a)

-4

b)

$-\frac{1}{4}$

c)

$\frac{1}{4}$

d)

4

70.

$125^x\cdot25^{2x+1}=\left(\frac{1}{5}\right)^{x+6}$

Solve.

a)

$-\frac{18}{6}$

b)

-1

c)

1

d)

$\frac{18}{6}$

71.

Solve.
$\left(\frac{1}{8}\right)^{3x}=\left(\frac{1}{8}\right)^{x+6}$

a)

1

b)

2

c)

3

d)

4

72.

Solve.
$3^{x^2+5}=27^{x+1}$

a)

-2,-1

b)

-2,1

c)

2,-1

d)

2,1

73.

Solve.
$4^{6-9x}=8^{x-3}$

a)

0

b)

1

c)

2

d)

3

74.

Solve.

4^{5x+2}=\left(\frac{1}{64}\right)

a)

-2

b)

-1

c)

1

d)

2

75.

$7^{3-x}=\left(\frac{1}{343}\right)^{ }$

a)

-6

b)

0

c)

1

d)

6

76.

Solve.
$\left(\frac{1}{216}\right)^{x-1}=36^x$

a)

-1

b)

$-\frac{3}{5}$

c)

$\frac{3}{5}$

d)

1

77.

How else can you write $\sqrt{x}$ ?

a)

$x^{\frac{1}{2}}$

b)

$x^2$

c)

$x^{-2}$

d)

$x^{\frac{1}{4}}$

78.

How else could you write $4^{-2}$ ?

a)

$16$

b)

$-16$

c)

$-\frac{1}{16}$

d)

$\frac{1}{16}$

79.

4^-½=

a)

2

b)

-2

c)

½

d)

-½

80.

(y⁹)^-2

a)

y¹⁸

b)

y¹¹

c)

1/y¹⁸

d)

y⁹/2

81.

Which of the following is equivalent to the expression $\frac{1}{2x^7}$ ?

a)

$\left(2x\right)^{-7}$

b)

$\frac{1}{2}x^7$

c)

$\frac{1}{2}x^{-7}$

d)

$2x^{-7}$

82.

\frac{2}{x^3}=?

a)

$2x^3$

b)

$2x^{-3}$

c)

$8x^3$

d)

$8x^{-3}$

83.

Simplify.

a)

y⁶⁰

b)

¹/_y¹⁶

c)

y^-16

d)

y⁴

84.

Simplify -9⁰

a)

1

b)

-1

c)

-9

d)

9

85.

Simplify

a)

-1/125

b)

125

c)

-125

d)

1/125

86.

Any number written to the 0 power is always 1

Example: 8⁰=1

a)

True

b)

False

c)

Sometimes

87.

Simplify 5^-2

a)

-10

b)

1/25

c)

1/(5)²

d)

-1/10

88.

5³x²y $\left(\frac{3412x^{20}a^b}{y^{421}z^{98}}\right)^0\ \ \$

a)

$125x^2y$

b)

125xy

c)

1

d)

5

89.

Simplify $\frac{-5p^0t^{-5}}{2^{-1}m^2}$

a)

$\frac{-5p}{2t^5m^2}$

b)

$\frac{10m^2}{t^5}$

c)

$\frac{\left(-5\right)^2}{t^5m^2}$

d)

$\frac{-10}{t^5m^2}$

90.

Solve $16^{x+2}=\frac{1}{256^x}$ .

a)

$x=-\frac{1}{4}$

b)

$x=\frac{1}{4}$

c)

$x=-\frac{2}{3}$

d)

$x=\frac{2}{3}$

91.

What is the value of $2^{3\ }\times2^{7\ }\times2^{10}+2^5\times2^{11}\times2^4$ ?

a)

$2^{20}$

b)

$2^{30}$

c)

$2^{21}$

d)

$2^{17}$

92.

Find the value of $(4a^3b^2)^2$ .

a)

$16a^6b^4$

b)

$8a^6b^4$

c)

$16a^9b^4$

d)

$8a^9b^4$

INDICES QUIZ

Total questions: 92

Worksheet time: 1hrs 25mins

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