(4x10^-5)^2(2.63x10^17)/6.7x10^3

Thankns Ninja,

OR you could just copy it into the site calculator!

$${\frac{{\left({\mathtt{4}}{\mathtt{\,\times\,}}{{\mathtt{10}}}^{-{\mathtt{5}}}\right)}^{{\mathtt{2}}}{\mathtt{\,\times\,}}\left({\mathtt{2.63}}{\mathtt{\,\times\,}}{{\mathtt{10}}}^{{\mathtt{17}}}\right)}{{\mathtt{6.7}}}}{\mathtt{\,\times\,}}{{\mathtt{10}}}^{{\mathtt{3}}} = {\mathtt{62\,805\,970\,149.253\: \!731\: \!343\: \!283\: \!582\: \!1}}$$

If I was going to do it more by hand.  I'm sure this is the same as Ninja, just presented a little differently.

$$\\\frac{(4 \times 10^{-5})^2(2.63 \times 10^{17})}{6.7} \times 10^3\\\\
\frac{16 \times 10^{-10}\times 2.63 \times 10^{17}}{6.7}\times 10^3 \\\\
\frac{16 \times 2.63}{6.7}\times 10^{
(3-10+17)} \\\\
6.28060\times 10^{
10} \qquad \mbox{Correct to 6 significant figures}\\\\$$

 

One of us has made a mistake Ninja.  Can you find it?

I found it  - you put 10^3 on the bottom and I put it one the top.

Both interpretations are valid.  That is why people need to use brackets (properly)!

Start by doing the first part.

(4x10^-5)^{^2}(2.63x10¹⁷)÷6.7x10³ 

Raising something to the second power means to multiply it by itself

(4x10^-5)(4x10^-5)(2.63x10¹⁷)÷6.7x10³        

Now we can do 4 x 4 and 10^-5 x 10^-5, as long as we multiply those two results together at the end.

For example, say we have (10x5)(10x5) Here we can multiply 10x10, then 5x5, then multiply them together.

10x10=100

5x5=25

100x25=2500

We'll get the same result if we multiply in the parentheses first.

(10x5)(10x5)

(50)(50) 

2500

So, this shows that we can multiply 4 x 4 and 10^-5 x 10^-5 next.

(4x10^-5)(4x10^-5)(2.63x10¹⁷)÷6.7x10³  

(4x4 x 10^-5x10^-5)(2.63x10¹⁷)÷6.7x10³    

(16 x 10^-5x10^-5)(2.63x10¹⁷)÷6.7x10³  

Remember, it we're multiplying numbers with exponets and they have the same base, we can add the exponets.

(16 x 10^-5x10^-5)(2.63x10¹⁷)÷6.7x10³

(16 x 10^(-5)+(-5))(2.63x10¹⁷)÷6.7x10³

(16 x 10^-10)(2.63x10¹⁷)÷6.7x10³

Now we can do the same thing with the next set of parentheses.

(16 x 10^-10)(2.63x10¹⁷)÷6.7x10³

(16x2.63  x 10^-10x10¹⁷)÷6.7x10³

(16x2.63  x 10^(-10)+(17))÷6.7x10³

(16x2.63  x 10^(-10)+(17))÷6.7x10³

(42.08x10⁷)÷6.7x10³

Now we still have basically the same rule, but we subtract the exponets because we are dividing

(42.08x10⁷)÷6.7x10³

(42.08÷6.7 x 10⁷÷10³)

6.280597 x 10^(7)-(3)

6.280597 x 10⁴

So that's our final answer, or, we could multipy this out.

6.280597 x 10⁴

6.280597 x (10)(10)(10)(10)

6.280597 x (10000)

62805.97