Being that you have 29 problems and I don't think anyone is willing to do your whole homework page, I'll leave you with this:
If you have an equation where two number share the same base (ex: [tex]10 ^{x} * 10 ^{y}[/tex]), you keep the base the same and add the exponents ([tex]10 ^{x+y}[/tex]). So your first problem 10^5 * 10^7 = 10^12.
Dividing with exponents is just the opposite. If two numbers share the same base but have different exponents (ex: [tex] \frac{10 ^{x} }{10 ^{y} } [/tex]), you keep the base the same and subtract the exponents ([tex]10 ^{x-y} [/tex]). If this yields a negative exponent, you send it to the denominator and it becomes positive (ex: [tex]10 ^{-2} = \frac{1}{10 ^{2}} [/tex])
When simplifying expressions where you have the exponent of an exponent (ex: [tex](10 ^{x}) ^{y}[/tex]), you multiply the exponents together to create one power ([tex]10 ^{x*y}[/tex]. Same rule with yielding negative exponents applies but you should be okay looking at your worksheet.
If you need additional help still you can send me a message or reply in a comment and I'll come back. Same for if you need me to do examples from your piece of paper.
