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How do you simplify # (16q^0 r^-6) /( 4q^-3 r^-7)#?

Answer 1

Genesis Allen

#(16q^0r^(-6))/(4q^(-3)r^(-7))=4q^3r#

with exclusions #q!=0# and #r!=0#

If #a != 0# and #b# and #c# are integers, then #a^b/a^c = a^(b-c)#

So:

#(16q^0r^(-6))/(4q^(-3)r^(-7))#

#=(16/4)(q^0/q^(-3))(r^(-6)/r^(-7))#

#=4 q^(0-(-3)) r^((-6)-(-7))#

#=4q^3r^1#

#=4q^3r#

with exclusions #q!=0# and #r!=0#

The exclusions are required since if #q=0# or #r=0# then at least one of #q^(-3)#, #r^(-6)#, #r^(-7)# is undefined.

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Answer 2

Isaiah Anthony

To simplify the expression (16q^0 r^-6) /( 4q^-3 r^-7), you can combine like terms in the numerator and denominator, and then simplify the exponents accordingly.

16q^0 r^-6 simplifies to 16r^-6, as any term raised to the power of zero equals 1.

4q^-3 r^-7 simplifies to 4q^3 r^7, by moving the negative exponents to the opposite side of the fraction and changing their signs.

Now, you can divide 16r^-6 by 4q^3 r^7. Divide the coefficients (16/4) and the variables (r^-6 / r^7).

16/4 equals 4.

r^-6 / r^7 simplifies to 1/r^(7-(-6)) = 1/r^13.

So, the simplified expression is 4/r^13.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.