MATH SOLVE

9 months ago

Q:
# 100a×1000b can be written in the form 10w.Show that w=2a+3b

Accepted Solution

A:

100^a x 1000^b

=(10^2)^a x (10^3)^b

By the laws of exponents, (x^a)^b = x^ab

=(10^2a) x (10^3b)

Also, since x^a * x^b = x^(a+b)

=10^(2a+3b)

If this is in the form 10^w,

w = 2a+3b

=(10^2)^a x (10^3)^b

By the laws of exponents, (x^a)^b = x^ab

=(10^2a) x (10^3b)

Also, since x^a * x^b = x^(a+b)

=10^(2a+3b)

If this is in the form 10^w,

w = 2a+3b