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This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.

When posting on Brilliant:

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## Comments

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TopNewestWhich one do you mean I or II :

$75^{40} = 9^{20 \times 5^{x}} . . . . . I$

$75^{40} = 9^{20} \times 5^{x} . . . . .II$

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no.2

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how do u type multiple again? tell me pls.

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You can see how to type in math formatting by click on "formatting guide" at the bottom-left corner of your comment box.

To type multiple, just type " \times " in math format (remember, in math format! See how to start a math format in the formatting guide.

The more easy ways to know the format of symbols, just point your cursor at the symbols, the format then will appears.

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the 2nd one

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Sorry for the late response,

$75^{40} = 9^{20} \times 5^{x}$

$75^{40} = (3^2)^{20} \times 5^{x}$

$75^{40} = 3^{40} \times 5^{x}$

$\frac{75^{40}}{3^{40}} = 5^{x}$

$(\frac{75}{3})^{40} = 5^{x}$

$25^{40} = 5^{x}$

$(5^2)^{40} = 5^{x}$

$5^{80} = 5^{x}$

$\boxed{x = 80}$

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$75^{40}= (3*25)^{40}$

$= 3^{40} * 25^{40}$

$= 3^{2*20} * (5^2)^{40}$

$= (3^2)^{20} * 5^{2*40}$

$= 9^{20}*5^{80}$

Therefore $x = 80$. I only used 2 formulae, $(ab)^n = a^n * b^n$ and $(a^n)^m = a^{m*n}$

Also, to write all the signs, read this

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$a^x \times a^y = a^{x+y}$

$(a^x)^y = a^{xy}$

So,

$3^{40} \neq 3^{20+2}$ but

$3^{40} = 3^{2 \times 20} = (3^2)^{20}$

Got it?

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$3^{20 \times 2}$. I used the $*$ symbol.

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x=80

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X=80

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