Simplify each expression, write your answers in index form.
a) 52 x 53 =5⁵ b) 64 x 63 =6⁷ c) 104 x 102 =10⁶ d) a2 x a2 x a3 =a⁷ e) 45 x 4 =4⁶
Simplify each expression, write your answers in index form where appropriate.
a) 25 x 23 =2⁸ b) 82 x 84 =8⁶ c) a3 x a2 =a⁵ d) 23 x 23 =2⁶ e) b3 x b4 =b⁸
3. Simplify each expression.
a) 35 ÷ 32 =3³ b) k4 ÷ k3 =k¹ c) 106 ÷ 104 =10² d) 52 ÷ 54 =5² e) 7 ÷ 71= 7⁰
4. a) Simplify each expression.
a) 22 ÷ 22 =2⁰ b) 22 ÷ 23 =2¹ c) 22 ÷ 24 d) 24 ÷ 22 e) 24 ÷ 26
5. Write each expression as a power or expression.
a) 83 x 84 b) 52 x 5 c) 42 x 44 d) 92 ÷ 93 e) 122 ÷ 124
11.a) Write each of these as a power of 2.
i) (22)2 ii) (22)3 iii) (24)2 iv) (24)3 v) (22)4
b) What can you say about (2m)n if m and n are positive integers?
Answers
Simplify each expression, write your answers in index form.
Solution :- using a^m * a^n = a^(m + n) in all 5 parts ,
a) 5² x 5³ = 5⁵
→ 5^(2 + 3) = 5⁵
→ 5⁵ = 5⁵
b) 6^4 x 6^ 3 =6⁷
→ 6^(4 + 3) = 6⁷
→ 6⁷ = 6⁷
c) 10^4 x 10^2 =10⁶
→ 10^(4 + 2) = 10⁶
→ 10⁶ = 10⁶
d) a^2 x a^2 x a^3 =a⁷
→ a^(2 + 2 + 3) = a⁷
→ a⁷ = a⁷
e) 4^5 x 4 =4⁶
→ 4^(5 + 1) = 4⁶
→ 4⁶ = 4⁶
Simplify each expression :-
Solution :- a^m ÷ a^n = a^(m - n)
a) 3^5 ÷ 3^2 =3³
→ 3^(5 - 2) = 3³
→ 3³ = 3³
b) k^4 ÷ k^3 =k¹
→ k^(4 - 3) = k¹
→ k¹ = k¹
c) 10^6 ÷ 10^4 =10²
→ 10^(6 - 4) = 10²
→ 10² = 10²
d) 5^2 ÷ 5^4 =5^(-2)
→ 5^(2 - 4) = 5^(-2)
→ 5^(-2) = 5^(-2)
e) 7 ÷ 7^1= 7⁰
→ 7^(1 - 1) = 7⁰
→ 7⁰ = 7⁰
Write each expression as a power or expression.
a) 8^3 x 8^4
→ 8^(3 + 4)
→ 8⁷
b) 5^2 x 5
→ 5^(2 + 1)
→ 5³
c) 4^2 x 4^4
→ 4^(2 + 4)
→ 4⁶
d) 9^2 ÷ 9^3
→ 9^(2 - 3)
→ 9^(-1)
e) 12^2 ÷ 12^4
→ 12^(2 - 4)
→ 12^(-2)
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