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What is the Law of exponent.

Sagot :

LAWS OF EXPONENTS

I. Product Of Powers

If the expressions multiplied have the same base, add the exponents.

[tex]x^{a} \: • \: x ^{b} = x^{a+b} [/tex]

II. Power Of A Power

If the expression raised to a number is raised by another number, multiply the exponents.

[tex](x^{a})^{b} = x^{ab}[/tex]

III. Power Of A Product

If the multiplied expressions is raised by a number, multiply exponents then multiply the expressions.

[tex](x^{a}x^{b})^{c} = x^{ac} \: x^{bc} \\ (xy)^{a} = x^{a} y^{a}[/tex]

IV. Quotient Of Power

If the ratio of two expressions is raised to a number, then

Case 1. [tex] \displaystyle \frac{x^{a}}{x^{b}} = \displaystyle x^{a+b}[/tex], where a > b.

Case 2. [tex] \displaystyle \frac{x^{a}}{x^{b}} = \displaystyle \frac{1}{x^{b-a}}[/tex], where a < b.

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