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Write the division as a fraction and cancel common factors.

Recall, negative indices mean you divided by more than you had, for example, $\\displaystyle \\frac{1}{12^3}$ can be written as $12^{-3}$.

In general, we have $\\displaystyle\\frac{a^b}{a^c}=a^{b-c}$.

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$u^\\var{powers1[0][0]}\\div u^\\var{powers1[1][0]}$ = [[0]]

Use ^ for powers. Input your answer in index form.

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Cancel common factors.

Recall, negative indices mean you divided by more than you had, for example, $\\displaystyle \\frac{1}{12^3}$ can be written as $12^{-3}$.

In general, we have $\\displaystyle\\frac{a^b}{a^c}=a^{b-c}$.

$\\displaystyle\\frac{x^\\var{powers2[0][0]}\\cdot x}{x^\\var{powers2[1][0]} \\cdot x^\\var{powers2[2][0]}}$ = [[0]]

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Since the bases are all the same ($w$) and we are dividing, we can simply subtract the powers.

In general, we have $\\displaystyle\\frac{a^b}{a^c}=a^{b-c}$.

$\\displaystyle\\frac{y^\\var{ndec}}{y^\\var{neg}}$ = [[0]]

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Use ^ for powers. Input your answer in index form.

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Use ^ for powers. Input your answer in index form.

It is important to note that the bases are different! Index laws only can be applied if the bases are the same (or can be made the same). Because of this we deal with the different bases separately.

Notice the first part of the expression can not be simplified using index laws.

$x^\\var{powers3[0][0]}\\times y^\\var{powers3[1][0]}$

However, with the division we can do some simplification. We can either:

write it as a fraction and cancel the common factor of $x^\\var{minpow4}$ from the top and bottom:
\\[\\frac{x^\\var{powers3[0][0]}\\times y^\\var{powers3[1][0]}}{ x^\\var{powers3[2][0]}}=\\frac{x^\\var{powers3[0][0]-minpow4}\\times y^\\var{powers3[1][0]}}{ x^\\var{powers3[2][0]-minpow4}}=x^\\var{diffpow4}y^\\var{powers3[1][0]}\\]
Subtract the powers, \"top power minus the bottom power\" for the terms with the same base:
\\[\\frac{x^\\var{powers3[0][0]}\\times y^\\var{powers3[1][0]}}{ x^\\var{powers3[2][0]}}=x^\\var{diffpow4}y^\\var{powers3[1][0]}\\]

$\\displaystyle\\frac{x^\\var{powers3[0][0]}\\cdot x^\\var{powers3[1][0]}}{x^\\var{powers3[2][0]}}$= [[0]]

Note: use * for multiplication.

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Use ^ for powers. Input your answer in index form.

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Use ^ for powers. Input your answer in index form.

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Is the following statement true or false?

$\\displaystyle\\frac{2z}{z^\\var{powers1[0][0]}} = 2^\\var{-powers1[0][0]}$

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It is important to note that the bases are different! Index laws only can be applied if the bases are the same (or can be made the same).

True

", "

False

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Is the following statement true or false?

$\\displaystyle\\frac{2a}{a^\\var{powers1[0][0]}} = 2^\\var{1-powers1[0][0]}$

It is important to note that the bases are different! Index laws only can be applied if the bases are the same (or can be made the same). We can only add the powers if the bases are the same.

True

", "

False

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Is the following statement true or false?

$\\displaystyle\\frac{2b}{b^\\var{powers1[0][0]}} = 2\\times b^\\var{1-powers1[0][0]}$

It is important to note that the bases are different! Index laws only can be applied if the bases are the same (or can be made the same). We can only add the powers if the bases are the same.

Note in this question we can make the bases the same.

\\[\\frac{2b}{b^\\var{powers1[0][0]}} = \\frac{2\\times b}{b^\\var{powers1[0][0]}} = 2\\times b^\\var{1-powers1[0][0]}\\]

True

", "

False

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Machten invoeren doe je zo 7^{-2} $7^{-2}$

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2..6

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