Mastering Algebra - Working With Exponents - Part Ii

Exponents - Mastering Algebra - Working With Exponents - Part Ii

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In Part I of this article, we discussed how to work with exponents, specifically how to simplify expressions which involved multiplying like bases, raising an exponent to someone else power, and the asset of any expression to the 0th and the 1st powers. Here we search for the distributive and quotient properties of exponents.

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Exponents

When you have an expression that involves one or more variables and numbers, and each of these may itself have an exponent, and then we have this expression enclosed in parentheses and raised to a power, you must use the distributive asset of exponents to simplify: thus (3x^2y^3)^3 would qualify as such an expression. To simplify this expression, we plainly multiply the exponent of each term by the exponent surface parentheses. Recall that the amount 3 term has the indiscernible demon exponent 1, and this was covered in the former article. Thus we derive 3^3x^6y^9, and simplifying for the amount term, 27x^6y^9. search for that we are distributing the exponent 3 surface the parentheses to each of the exponents inside parentheses, thus the name distributive property. Looking at someone else example, take (2^2x^4y^6z^3)^4. Distributing the 4 over the inside exponent terms and multiplying we have 2^8x^16y^24z^12 and simplifying for the amount term we have 256x^16y^24z^12.

The quotient asset comes into play when we divide one expression containing like bases by another. For example, take the expression (x^6y^3)/(x^2y^2). To simplify this expression, we subtract the exponents of like bases: thus x^4y^1 or more plainly x^4y is the resulting expression. Again to understand why this asset works the way it does, let us return to the analogy of pearls on a string, which we employed in Part I of this article. If we write out (x^6y^3)/(x^2y^2) we have xxxxxxyyy/xxyy. Now using the cancellation property, we can assault 2 x-pearls and 2 y-pearls from the numerator to end up with our acknowledge of 4 x-pearls and 1 y-pearl, namely x^4y.

That is all there authentically is to these two properties. To make anyone more out of them would plainly be complicating something unnecessarily. Remember: mathematics is hard in itself; yet there is a lot to this field which is effortlessly understandable, such as the properties outlined in these two articles. Learn these rules and become customary with their uses, as then mastery to algebra will be right around the corner.

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