Essential Prealgebra Skills Practice Workbook by Chris McMullen
Author:Chris McMullen [McMullen, Chris]
Language: eng
Format: epub
Publisher: Zishka Publishing
Published: 2020-04-23T17:00:00+00:00
xmxn = xm+n
For example, with m = 3 and n = 4 we get x3x4 = x7. For x = 2, observe that:
23 = 2∙2∙2 = 8
24 = 2∙2∙2∙2 = 16
27 = 2∙2∙2∙2∙2∙2∙2 = 128
23∙24 = 8∙16 = 128 = 27
Recall that a middle dot (·) or parentheses may be used to multiply numbers.
Why does xmxn = xm+n? Consider the case x = 10, for which 10m∙10n = 10m+n. This holds because 10m tells you how many 10’s to multiply together. Note that 10m has m zeroes after the one. For example, 104 = 10∙10∙10∙10 = 10,000 has 4 zeroes after the one. Since 10m+n has m + n zeroes after the one, it will equal 10m∙10n. More generally, note that xm tells you have many x’s are multiplying together. For example, x3 = xxx. (Recall that no symbol is used to indicate multiplication between variables.) Since m + n is how many x’s are multiplying together in xm+n, it will equal xmxn. For example, x2 = xx, x3 = xxx, and x5 = xxxxx, which agrees with x2 x3 = xxxxx = x5 = x2+3.
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