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This is too large a number for most calcs to handle.

But a good approximation can be found this way.

$$8255^{33}\\\\
=(8255^{11})^3 \\\\
\approx (1.213075562 \times 10^{43})^3\\\\
\approx(1.213075562 \times 10^{43})^3\\\\
\approx(1.213075562^3) \times 10^{43*3}\\\\
\approx 1.785104155\times 10^{129}\\\\$$

It is the wavelength of light that is measured in nm not luminosity!

nm stands for nanometres.  A nanometre is 10^-9 metres.

Your solution should have 600*10^-9 in it, not 600*10⁺⁹.  The resulting thickness is then given in metres (m).  If you leave out the 10^-9  the resulting thickness would be in nanometres (nm).

625 = 5³*5 so its cube root is 5√5

135 = 3³*5 so its cube root is 3√5

Therefore  5 ³√625 + ³√135 = 5*5√5 + 3√5 = 25√5 + 3√5 = 28√5

x²+6x+2 factors nicely: (x+4)(x+2)

3x²+7x+2 also factors nicely:  (3x+1)(x+2)

The x+2 term is common to both, so it cancels from the original ratio which simplifies to (x+4)/(3x+1)

25^(4x-2) = 125^(3x-1)

(5²)^(4x-2) = (5³)^(3x-1)

5^2(4x-2) = 5^3(3x-1)

2(4x-2) = 3(3x-1)

8x - 4 = 9x - 3

-x = 1

x = -1

You could use the calculator on the home page here to solve this:

$$3\sqrt{180}+\sqrt[2]{5}\\\\
=3\sqrt{36*5}+\sqrt{5}\\\\
=3*6\sqrt{5}+\sqrt{5}\\\\
=18\sqrt{5}+\sqrt{5}\\\\
=19\sqrt{5}\\\\$$

Thank you novice, that is a great answer.  

Sorry don't know how to write superscript so using the "^" sign.

a 7⁄8 * a ‾ 3⁄4

since the base is same, add the powers

= a ^(7/8 - 3/4)

= a ^(1/8)

5√2048 + 5*5√2 

= 5√2*1024 + 5*5√2 

= 5√2*32*32 + 5*5√2 

= 5*32√2 + 5*5√2 

=(160+25)*√2

=185√2

1 US Dollar = 3.43 Israeli new shekel

So, 5 US dollars = 17.15 Israeli new shekel

A mathematical function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output.

We can use scientific notation here:

[ 1.5 x 10¹² ] / [ 7 x 10⁹ ] = [ 15 x 10¹¹ ] / [ 7 x 10⁹ ] ≈ 2.1428 x 10² ≈ $ 214.28

4√32 +4√50-2√8 

=4*4*sqrt(2)+4*5*sqrt(2)-2*2*sqrt(2)

=16*sqrt(2)+20*sqrt(2)-4*sqrt(2)

=32*sqrt(2)

I hope it helps.

Note 5√2048  =  5*[2⁵ √2] = 5 [32 √2] = 160√2

I assume 5^5√2 is supposed to be  (5^5)√2 =  3125√2

So we have  160√2 + 3125√2  =  3285√2

4 ³√54 +³√250 =

4 [³√(27*2)] +³√(125*2) =

4 [3 ³√(2)] + 5 [³√(2)] =

12 [ ³√(2)] + 5 [³√(2)]  =

17 ³√(2)