exponent

Exponentiation is an operation involving two numbers - the base and the exponent.

Division was a lie. Just like how subtraction was a lie. Because $2÷7=2\cdot 7^{-1}$.
Square root was also a lie. It’s just an exponent. Because $\sqrt[2]{7}=7^{\frac{1}{2}}$ and $\sqrt[3]{7}=7^{\frac{1}{3}}$.

Exponent identities.

$a^0=1$

$a^1=a$

$(ab{)}^c=a^c{b}^c$

$(a\cdot b{)}^c=a^c\cdot b^c$

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==$(a \cdot b)^{c}$== = ==$a^{c} \cdot b^{c}$==

$a^b\cdot a^c=a^{b+c}$

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==$a^{b}\cdot a^{c}$== = ==$a^{b+c}$==

$(a^b{)}^c=a^{bc}$

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==$(a^{b})^{c}$== = ==$a^{bc}$==

$(\frac{a}{b}{)}^c=\frac{a^c}{b^c}$

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==$(\dfrac{a}{b})^c$== = ==$\dfrac{a^c}{b^c}$==

$\frac{a^b}{a^c}=a^{b-c}$

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==$\dfrac{a^{b}}{a^{c}}$== = ==$a^{b-c}$==

$a^{-b}=\frac{1}{a^b}$

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==$a^{-b}$== = ==$\dfrac{1}{a^{b}}$==

$(a+b{)}^2=a^2+2ab+b^2$

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==$(a+b)^2$== = ==$a^2+2ab+b^2$==

$a^2-b^2=(a+b)(a-b)$

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==$a^2-b^2$== = ==$(a+b)(a-b)$==

$a^3+b^3=(a+b)(a^2-ab+b^2)$

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==$a^3+b^3$== = ==$(a+b)(a^2-ab+b^2)$==

$a^3-b^3=(a-b)(a^2+ab+b^2)$

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==$a^3-b^3$== = ==$(a-b)(a^2+ab+b^2)$==

More!

${\left(\frac{a}{b}\right)}^c=a^c\cdot b^{-c}$

${\left(\frac{a}{b}\right)}^c=\frac{(a{)}^c}{(b{)}^c}=(a{)}^c\cdot {\left(\frac{1}{b}\right)}^c=a^c\cdot b^{-c}$

$a^2+ba={\left(a+\frac{b}{2}\right)}^2-{\left(\frac{b}{2}\right)}^2$

$a^2+ba+c=a{\left(b-(-\frac{b}{2a})\right)}^2+\left(c-\frac{b^2}{4a}\right)$