2 years ago

Help its pre-algebra haha help plz

Mathematics

1 answer:

maks197457 [2]2 years ago

8 0

Answer:

8 ramen bowls

4 pho bowls

Step-by-step explanation:

12-4=8

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Which expression is equivalent to ( 4mn / m^-2n^6)^-2

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Here are a few rules with exponents that apply here:

Raising a power to a power: $(x^m)^n=x^{m*n}$
Dividing exponents of the same base: $\frac{x^m}{x^n}=x^{m-n}$
Converting negative exponents to positive ones: $x^{-m}=\frac{1}{x^m}\ \textsf{and}\ \frac{1}{x^{-m}}=x^m$

Firstly, solve the outer exponent:

$(\frac{4mn}{m^{-2}n^{6}})^{-2}=\frac{4^{-2}m^{-2}n^{-2}}{m^{-2*-2}n^{6*-2}}=\frac{4^{-2}m^{-2}n^{-2}}{m^4n^{-12}}$

Next, divide:

$\frac{4^{-2}m^{-2}n^{-2}}{m^4n^{-12}}=4^{-2}m^{-2-4}n^{-2-(-12)}=4^{-2}m^{-6}n^{10}$

Next, convert the negative exponents:

$4^{-2}m^{-6}n^{10}=\frac{n^{10}}{4^2m^6}=\frac{n^{10}}{16m^6}$

<u>Your final answer is n^10/16m^6 , or B.</u>

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