100a*1000b can be written in the form 10w. Show that w=2a+3b

Question

Mathematics

Kianna Bolton

13 February, 13:07

100a*1000b can be written in the form 10w. Show that w=2a+3b

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Answers (2)

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Emelia Lane · Answer 1

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

Kiley Neal · Answer 2

I was wondering, what exactly is this topic called?