Question

All exponents law or formula

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Answer 1

$\huge {\textbf {\underline {\underline {ANSWER}}}}$

$\textbf {\underline {Exponents Law and Formulas }}$

●

$a \times a \times a \times a ... \times \: n \: times \: of \: a \: = {a}^{n}$

The repeated multiplication is represented by the term exponent.

e.g.

3 × 3 × 3 × 3 = 3^4

●

${a}^{m} . {a}^{n} = {a}^{m + n}$

For Multiplication of exponent with same bases , we write the Base once and add the Exponents

e.g.

3^2 . 3^3 = 3^2+3 = 3^5

●

$\frac{ {a}^{m} }{ {a}^{n} } = {a}^{m - n}$

For division of exponents with same bases , we write base once and subtract the exponents.

e.g.

$\frac{ {3}^{3} }{3} = {3}^{3 - 1} = {3}^{2}$

●

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

If the denominator has a exponents with negative index it becomes positive on numerator and vise versa.

e.g.

$\frac{1}{ {3}^{ - 2} } = {3}^{2}$

●

${a}^{0} = 1$

zero raised to any number is one.

e.g.

${3}^{0} = 1$

●

${a}^{1} = a$

Any number raised to one is number itself.

${3}^{1} = 3$

$log( {a}^{m} ) = m log(a)$

$\frac{d}{dx} \: of \: {x}^{n} = n. {x}^{n - 1}$

Thanks.

Answer 2

$\huge\mathfrak{Ello\:Mate}$❤

Following are the laws of exponents:

${a}^{m} \times {a}^{n} = {a}^{mn} \\ {( {a}^{m} )}^{n} = {a}^{mn} \\ {a}^{m} \div {a}^{n} = {a}^{m - n} \\ {a}^{0} = 1 \\ {a}^{ - m} = \frac{1}{m}$

Hope it helps uhh✌

$\bold{@PhilophobiaXD}$