Algebra I: Multiplying and dividing different bases with the same exponent
 This is a free lesson from our course in Trigonometry In this lesson you'll learn (with the help of several examples) how to multiply and divide different bases with the same exponent. If the bases are different but the exponents are the same, then you can combine them. For example : (xł)(ył) = (x)(x)(x)(y)(y)(y). But you know that it doesn’t matter what order you do your multiplications in or how you group them. Therefore, (x)(x)(x)(y)(y)(y) = (x)(y)(x)(y)(x)(y) = (xy)(xy)(xy). But from the very definition of powers, you know that’s the same as (xy)3. And it works for any common power of two different bases: All the laws of exponents work in both directions. If you see (4x)3 you can decompose it to (43)(x3), and if you see (43)(x3) you can combine it as (4x)3. dividing different bases can’t be simplified unless the exponents are equal. x3÷y2 can’t be combined because it’s just xxx/yy; But x3÷y3 is xxx/yyy, which is (x/y)(x/y)(x/y), which is (x/y)3.
Other useful lessons:
 Multiplying and dividing two numbers with same base and different exponents Calculating and working with zero exponents Calculating and working with negative exponents Calculate the root Convert between radicals and fractional exponents
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