How do you do this math question ten exponent nine equals ten times ten exponent x divided by 10 exponent minus 3 what should x be Please help you understand it?

Answer 1

10^9 = 10*10^x/10^(-3)

Some index laws:

L1: a^1 = a

L2: a^x * a^y = a^(x+y)

L3: a^(-x) = 1/a^x

These are not all the index laws and you will need to know them all to understand exponents. But for now, these are the only ones you need.

Now,

10*10^x = 10^1 * 10^x [using L1 for 10=10^1]

= 10^(1+x) [using L2]

Therefore 10*10^x/10^(-3) can be rewritten as 10^(1+x)/10^(-3)

= 10^(1+x)/ (1/10^(3)) [using L3 on 10^(-3)]

= 10^(1+x) * 10^(3) [division by any number = multiplication by its reciprocal] = 10^(1+x+3) [using L2]

= 10^(x+4) [simplifying inside the parentheses]

So we have 10^9 = 10^(x+4)

this implies 9 = x + 4

and so x = 5.