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4 years ago

6

N is a positive integer. Explain why n(n-1) must be an even number.

1 answer:

svetoff [14.1K]4 years ago

4 0

If N is a positive integer, it must be either even or odd. If N is odd, then N-1 will be even. If N is even, then N-1 will be odd. Either way, when you multiply n and n-1, one of those expressions is going to be an even number, and any number multiplied by an even number is an even number. Hope this helps! :)

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<img src="https://tex.z-dn.net/?f=%5Cfrac%7B%283a%5E2b%29%5E3%7D%7B9%28ab%29%5E4%7D" id="TexFormula1" title="\frac{(3a^2b)^3}{9(

VladimirAG [237]

You first multiply the outside exponents into the numbers in the parentheses.

When you have an exponent being multiplied directly to another exponent, you multiply the exponents together.

For example(because I am a bad explainer):

$(x^{2} )^4= x^{2(4)} = x^8$

$(x^4)^3 = x^{4(3)} = x^{12}$

When you divide an exponent by an exponent, you subtract the exponents

For example:

$\frac{x^4}{x^1} =x^{4-1}=x^3$

When you have a negative exponent, you move it to the other side of the fraction to make the exponent positive

For example:

$x^{-3}=\frac{1}{x^3}$

$\frac{1}{y^{-5}}=\frac{y^5}{1}=y^5$

$\frac{(3a^2b)^3}{9(ab)^4}$

You can think of it like this if you want:

$\frac{(3^1a^2b^1)^3}{9(a^1b^1)^4}$ Now multiply the outside exponents into the exponents in the parentheses

$\frac{3^3a^6b^3}{9(a^4b^4)} =\frac{27a^6b^3}{9(a^4b^4)}$ Divide 27 and 9

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Your answer is $\frac{3a^2}{b}$

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