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Number - Indices

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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


Answer the following:

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


Answer the following:

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