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How do you simplify #(m^6r^5p^3)/(m^5r^2p^3)#?

Answer 1

See the entire simplification process below:

We will use this rule for exponents to simplify this expression:

#x^color(red)(a)/x^color(blue)(b) = x^(color(red)(a)-color(blue)(b))#

#(m^color(red)(6)r^color(red)(5)p^color(red)(3))/(m^color(blue)(5)r^color(blue)(2)p^color(blue)(3)) = m^(color(red)(6)-color(blue)(5))r^(color(red)(5)-color(blue)(2))p^(color(red)(3)-color(blue)(3)) = m^1r^3p^0#

Now, we will use these two rules for exponents to complete the simplification:

#a^color(red)(1) = a# and #a^color(blue)(0) = 1#

#m^color(red)(1)r^3p^color(blue)(0) = mr^3 xx 1 = mr^3#

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Answer 2

Eli Assouline

To simplify the expression (m^6r^5p^3)/(m^5r^2p^3), you divide the coefficients and then divide the variables with the same base by subtracting their exponents. So, the simplified expression is (m^(6-5)r^(5-2)p^(3-3)) = m^1r^3p^0. Simplifying further, p^0 equals 1, so the final simplified expression is m^1r^3.

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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.