Question

How can you rewrite the expression so that both powers are 108?
(8.9 x 10) (4.4 x 107) = (8.9 x 10°) 8.64 X 10%)
4.4
X
107
÷10
× 10
? X
108

Answer 1

I need to know the exponent on the first 10 (the expression you wrote is a bit unclear). In general, though, to rewrite any number a×10^m so its power is 10^8 you do:

a×10^m = (a × 10^(m−8)) × 10^8.

So, for the second factor in your example:
4.4×10^7 = (4.4 × 10^(7−8)) × 10^8 = 0.44 × 10^8.

If the first factor is, for example, 8.9×10^0, then
8.9×10^0 = (8.9 × 10^(0−8)) × 10^8 = 8.9×10^−8 × 10^8 = 0.000000089 × 10^8.

If the first factor were 8.9×10^1, then
8.9×10^1 = (8.9 × 10^(1−8)) × 10^8 = 8.9×10^−7 × 10^8 = 0.00000089 × 10^8.

Tell me the missing exponent on the first term and I’ll finish the rewrite and compute the product.

Answer 2

dih