Question

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

Answer 1

To simplify and write the expressions in index form, we apply the rules of exponents. The answers are: a) 8192 b) 16777216 c) a^5 d) 64 e) b^7

Step-by-step explanation:

To simplify each expression and write the answers in index form, we need to apply the rules of exponents. Let's go through each expression:

a) 25 x 23 = (2^2)^5 x (2^3) = 2^(2x5) x 2^3 = 2^10 x 2^3 = 2^13 = 8192

b) 82 x 84 = (8^2)^2 x (8^4) = 8^(2x2) x 8^4 = 8^4 x 8^4 = 8^8 = 16777216

c) a3 x a2 = a^(3+2) = a^5

d) 23 x 23 = (2^3)^2 = 2^(3x2) = 2^6 = 64

e) b3 x b4 = (b^3) x (b^4) = b^(3+4) = b^7