laws of indices: 3.2 * 10^(-4) + 0.07 * 10^(-2),...

[Meezus123]

Hello, I'm trying to complete this homework but I'm not really sure how.

Perform the operation and write the result in standard form. Do not use a calculator to answer this question. Show your working, in particular how you manipulate the powers of 10.

(a) \(\displaystyle 3.2\, \times\, 10^{-4}\, +\, 0.07\, \times\, 10^{-2}\)

(b) \(\displaystyle \dfrac{6\, \times\, 10^{-5}\, \times\, (0.03\, \times\, 10^8)^2}{12\, \times\, 10^{-3}}\)

Using the laws of indices:

(a) write as a power of 2: \(\displaystyle \,8^2\, \times\, 2^{-3}\)

(b) write as a power of 3: \(\displaystyle \, \dfrac{3^{-5}\, \times\, 27}{9^2}\)

For the first set of questions I'm slightly confused. I believe its something to do with exponent laws.
I've currently got 3.2 - 0.07 = 3.13
10^-4 X 10^{-2 =} 10^-6
3.12 x 10^-6
is this correct?

For the second set of questions Im not sure how to even start calculating it. i've looked for a exponent law which uses different base and different power one being negative and had no luck could anyone help

 

[ksdhart]

For both parts, the trick does lie in an exponent law. Specifically, that a^-b = a/(a^b). So for part a, what if you rewrite both the negative exponents? Then you have two fractions you can add.

Then for part b, after making the appropriate revisions, you have a fraction in the denominator. Do you remember how to deal with that?

 

[lookagain]

Hello, I'm trying to complete this

< link to objectionable page removed >

homework but I'm not really sure how.
For the first set of questions I'm slightly confused. I believe its something to do with exponent laws.

I've currently got 3.2 - 0.07 \(\displaystyle \ \ \ \ \)You are not to combine those as is, and it's an addition
in the problem, anyway.
= 3.13

\(\displaystyle \ \ \ \ \) This is true, but it doesn't apply here. -----> 10^-4 X 10^{-2 =} 10^-6

3.12 x 10^-6

is this correct? \(\displaystyle \ \ \ \ \)No.

For the second set of questions Im not sure how to even start calculating it. i've looked for a exponent law which uses different base
and different power one being negative and had no luck could anyone help

\(\displaystyle 3.2*10^{-4} \ + \ 0.07*10^{-2} \ =\)

\(\displaystyle 3.2*10^{-4} \ + \ 0.07*[10^{-2}]*(100/100) \ = \)

\(\displaystyle 3.2*10^{-4} \ + \ (100)0.07*[10^{-2}]/100 \ = \)

\(\displaystyle 3.2*10^{-4} \ + \ 7*10^{-4} \ = \ ? \)