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 : (x³)(y³) = (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 (4^{3})(x^{3}), and if you see (4^{3})(x^{3}) you can combine it as (4x)^{3}.
dividing different bases can’t be simplified unless the exponents are equal.
x^{3}÷y^{2} can’t be combined because it’s just xxx/yy; But x^{3}÷y^{3} is xxx/yyy, which is (x/y)(x/y)(x/y), which is (x/y)^{3}.
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