Number - Indices

a - answer    s - solution    v - video

Question 1

Identify the base and the index (power or exponent) in the following:

a) $3^2$a s v
b) $4^9$a s v
c) $1^6$a s v
d) $7^{11}$a s v
e) $0.5^{3}$a s v
f) $6^{0.2}$a s v
g) $10^{\frac13}$a s v
h) $(-6)^1$a s v

Question 2

Write the following in index form (e.g. in the form $2^6$)

a) $3\times3$a s v
b) $4\times4\times4$a s v
c) $2\times2$a s v
d) $7\times7\times7\times7$a s v
e) $8\times8\times8\times8\times8$a s v
f) $2\times2\times2\times2\times2\times2\times2\times2$a s v
g) $16\times16\times16$a s v
h) $8$a s v

Question 3

Write the following as a multiplication

a) $5^2$a s v
b) $12^2$a s v
c) $4^3$a s v
d) $7^4$a s v
e) $9^5$a s v
f) $11^3$a s v
g) $6^1$a s v
h) $8^6$a s v

Question 4

Evaluate:

a) $2^3$a s v
b) $5^2$a s v
c) $7^2$a s v
d) $3^3$a s v
e) $2^5$a s v
f) $11^2$a s v
g) $4^3$a s v
h) $2^7$a s v

Question 5

a) Write $8$ in index form with base $2$a s v

b) Write $9$ in index form with base $3$a s v

c) Write $49$ in index form with base $7$a s v

d) Write $64$ in index form with base $4$a s v

e) Write $81$ in index form with base $3$a s v

f) Write $81$ in index form with base $9$a s v

g) Write $4$ in index form with base $4$a s v

h) Write $256$ in index form with base $2$a s v

Question 6

Collect like terms and write in index form:

a) $7\times3\times7\times3$a s v
b) $5\times4\times4\times5\times5$a s v
c) $6\times11\times11\times11\times6$a s v
d) $5\times7\times9\times7\times9$a s v
e) $8\times3\times5\times3\times5\times8\times8\times8$a s v
f) $2\times2\times3\times2\times2\times7$a s v
g) $18\times25\times25\times7\times25\times25\times18$a s v
h) $91\times100\times3\times11\times3\times100\times91\times3$a s v

Question 7

Are the following equal? Can you explain why?

a) $3^2\times3^4$ and $3^6$a s v
b) $5^2\times5^6$ and $5^8$a s v
c) $7^3\times7^2$ and $7^6$a s v
d) $2^3\times2^5$ and $2^8$a s v
e) $6^2+6^3$ and $6^5$a s v
f) $8^3+8^4$ and $8^{12}$a s v

Question 8

Are the following equal? Can you explain why?

a) $5^6\div5^2$ and $5^4$a s v
b) $7^8\div7^2$ and $7^4$a s v
c) $4^3\div4^1$ and $4^2$a s v
d) $10^8\div10^4$ and $1^2$a s v
e) $4^5-4^2$ and $4^3$a s v
f) $15^{10}-5^7$ and $10^3$a s v

Question 9

Are the following equal? Can you explain why?

a) $\left(4^2\right)^3$ and $4^6$a s v
b) $\left(4^2\right)^3$ and $4^8$a s v
c) $\left(2^3\right)^3$ and $2^9$a s v
d) $3^{2^3}$ and $3^8$a s v
e) $5^{3^2}$ and $5^6$a s v

Question 10

Simplify:

a) $5^2\times5^3$a s v
b) $7^1\times7^4$a s v
c) $8^4\times8^{10}$a s v
d) $3^3\times3^3$a s v
e) $7^{11}\times7^{25}$a s v
f) $4^3\times4^2\times4^5$a s v
g) $5^{16}\times5^2\times5^{20}$a s v
h) $8^2\times8^{99}\times8^{41}$a s v

Question 11

Simplify:

a) $9^5\div9^2$a s v
b) $5^9\div5^4$a s v
c) $7^{11}\div7^5$a s v
d) $\frac{11^5}{11^2}$a s v
e) $\frac{20^{44}}{20^4}$a s v
f) $17^{10}\div17^2\div17^5$a s v
g) $101^{77}\div101^{17}\div101^{15}$a s v
h) $823^{455}\div823^{133}\div823^{67}$a s v

Question 12

Simplify:

a) $\left(2^5\right)^2$a s v
b) $\left(3^6\right)^3$a s v
c) $\left(11^3\right)^4$a s v
d) $\left(4^6\right)^7$a s v
e) $\left(10^6\right)^9$a s v
f) $\left(\left(3^2\right)^4\right)^2$a s v
g) $\left(\left(4^5\right)^3\right)^4$a s v
h) $\left(2^5\right)^2$a s v

Question 13

Write without indices:

a) $3^{-1}$a s v
b) $4^{-1}$a s v
c) $6^{-1}$a s v
d) $8^{-1}$a s v
e) $10^{-1}$a s v
f) $26^{-1}$a s v

Question 14

Write without indices:

a) $3^{-2}$a s v
b) $5^{-2}$a s v
c) $8^{-2}$a s v
d) $2^{-3}$a s v
e) $4^{-3}$a s v
f) $3^{-4}$a s v
g) $2^{-5}$a s v
h) $3^{-5}$a s v

Question 15

Write without indices:

a) $9^{\frac12}$a s v
b) $16^{\frac12}$a s v
c) $49^{\frac12}$a s v
d) $64^{\frac12}$a s v
e) $100^{\frac12}$a s v
f) $169^{\frac12}$a s v

Question 16

Write without indices:

a) $8^{\frac13}$a s v
b) $27^{\frac13}$a s v
c) $16^{\frac14}$a s v
d) $1^{\frac12}$a s v
e) $64^{\frac13}$a s v
f) $32^{\frac15}$a s v

Question 17

Write without indices:

a) $8^{\frac23}$a s v
b) $27^{\frac23}$a s v
c) $64^{\frac23}$a s v
d) $16^{\frac34}$a s v
e) $32^{\frac35}$a s v
f) $81^{\frac34}$a s v
g) $1^{\frac25}$a s v
h) $128^{\frac37}$a s v

Question 18

Write without indices:

a) $9^{-\frac12}$a s v
b) $81^{-\frac12}$a s v
c) $25^{-\frac12}$a s v
d) $64^{-\frac13}$a s v
e) $125^{-\frac13}$a s v
f) $81^{-\frac14}$a s v
g) $125^{-\frac23}$a s v
h) $729^{-\frac23}$a s v

Question 19

Write without indices:

a) $2^0$a s v
b) $6^0$a s v
c) $20^0$a s v
d) $824^0$a s v
e) $0.2^0$a s v
f) $1.83^0$a s v
g) $\left(-1\right)^0$a s v
h) $\left(-10\right)^0$a s v
i) $\left(-\frac14\right)^0$a s v
j) $\left(\sqrt2\right)^0$a s v

Question 20

Write without indices:

a) $\left(-2\right)^2$a s v
b) $\left(-5\right)^2$a s v
c) $\left(-3\right)^3$a s v
d) $\left(-4\right)^3$a s v
e) $\left(-2\right)^4$a s v
f) $\left(-3\right)^4$a s v
g) $\left(-2\right)^{-1}$a s v
h) $\left(-3\right)^{-1}$a s v
i) $\left(-2\right)^{-2}$a s v
j) $\left(-5\right)^{-2}$a s v
k) $\left(-3\right)^{-3}$a s v
l) $\left(-4\right)^{-4}$a s v
m) $\left(-8\right)^{\frac13}$a s v
n) $\left(-32\right)^{\frac15}$a s v
o) $\left(-125\right)^{\frac13}$a s v
p) $\left(-8\right)^{\frac23}$a s v
q) $\left(-27\right)^{\frac23}$a s v
r) $\left(-64\right)^{-\frac13}$a s v
s) $\left(-125\right)^{-\frac13}$a s v
t) $\left(-8\right)^{-\frac23}$a s v
u) $\left(-32\right)^{-\frac45}$a s v

Question 21

a) What is $\left(-1\right)^2$?a s v

b) What is $\left(-1\right)^3$?a s v

c) What is $\left(-1\right)^4$?a s v

d) What is $\left(-1\right)^5$?a s v

e) Using this information can you find $\left(-1\right)^{18}$?a s v

f) What is $\left(-1\right)^{27}$?a s v

g) What is $\left(-1\right)^{104}$?a s v

h) What is $\left(-1\right)^{2815}$?a s v

i) What pattern have you found here?a s v