How to simplify using the exponent laws

Mathematics

1 answer:

Alinara [238K]3 years ago

3 0

Okay so you subtract if there is division and u add when there is multiplying
Ex
m14n13/ (m3)3n5
You would first add the 3s as it is multiplying which will give u m14n13/m6n5 and now you will subtract them. M will subratact with M and n will subtarct with n
14-6 and 13-5 which will give u m8n8

Now u have m8n8 divide by m2n4 so u subtract them whicch will give u m6n4

Now u leave that and solve your second division. M subtract m and n subtract n which will give m2n4.

Now you have m6n4 x m2n4. You will add them as it is multiplying. Your answer will be m8n8. M8n8 is your final answer

Didn’t mention before but u add and subtract the exponents

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Vaselesa [24]

It can work well here to simplify inside parentheses first.

$\displaystyle\left(\frac{4x^{-2}y^{2}}{12x^{-4}y^{-1}}\right)^{3}=\left(\frac{4}{12}x^{(-2-(-4))}y^{(2-(-1))}\right)^{3}\\\\=\left(\frac{x^{2}y^{3}}{3}\right)^{3}=\frac{x^{(2\cdot 3)}y^{(3\cdot 3)}}{3^{3}}\\\\=\frac{x^{6}y^{9}}{27}$