Question

$\large{\sf{\underline{\underline\pink{Question!!}}}}$
WRITE LAWS OF EXPONENTS
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– Non-copied Answer
– Well-explained Answer​

Answer 1

Please see the detailed answer in picture.

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Answer 2

★ Concept :-

Here the concept Laws of Exponents has been used. Here we shall gonna discuss about all the basic laws of Exponents and how to work and solve sums using them.

Let's do it !!

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★ Solution :-

$\;\bf{1.)\;\;\red{(x^{m})^{n}\;=\;x^{m.n}}}$

We see that the exponential term is multiplied by another Exponent. This means the resultant will be the base term raised to the product of Exponents.

For example :-

» (2²)³ = 64 = 2²˙³ = 2⁶ = 64

Clearly the terms come out to be equal. So this Exponent is correct.

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$\;\bf{2.)\;\;\blue{x^{m}\:\times\:x^{n}\;=\;x^{m\:+\:n}}}$

We see that the exponential term is multiplied by another exponential term but with same base in both. So the Exponents get added but the base remains same in resultant value.

For example :-

» 2² × 2³ = 4 × 8 = 32 = 2²⁺³ = 2⁵ = 32

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$\;\bf{3.)\;\;\green{\dfrac{x^{m}}{x^{n}}\;=\;x^{m\:-\:n}}}$

We see that there is a fraction given whose numerator and denominator have Exponents bur we see that base of both the exponential term term is equal. So we will subtract the Exponent of denominator from the Exponent of numerator but base will be same.

For example :-

» 2⁴ / 2³ = 16/8 = 2 = 2⁴¯³ = 2¹ = 2

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$\;\bf{4.)\;\;\orange{x^{-1}\;=\;\dfrac{1}{x}}}$

Here we see that whenever there is negative integer in the Exponent term then in order to make the Exponent in positive integer, we take the reciprocal of that base.

For example :-

» 2¯² = 1/2² = 1/4

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$\;\bf{5.)\;\;\pink{(xy)^{m}\;=\;x^{m}y^{m}}}$

Here the Exponent power gets divided between the terms. But the resultant and initial values remains same.

For example :-

» (2×3)² = 6² = 36 = 2² × 3² = 4 × 9 = 36

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$\;\bf{6.)\;\;\purple{x^{1/2}\;=\;\sqrt{x}}}$

Here the Exponent which is in fraction when applied to a base, then the denominator increases the root of the base and numerator of Exponent raises the base to that power.

For example :-

» 2^¾ = ⁴√2³

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