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How do you simplify #\frac { b ^ { 2} c ^ { 8} } { b c ^ { 0} \cdot b ^ { - 1} c ^ { 7} }#?

Answer 1

Anna Allen

#color(blue)(b^2c#

Given:

#(b^2*c^8)/(b*c^0*b^(-1)*c^7)#

#rArr (b^2*c^7*c^1)/(b*1*(1/b)*c^7)#

#rArr (b^2*c^7*c^1)/(b*1/b*c^7)#

#rArr (b^2*cancel c^7*c^1)/(cancel b*1/ cancel b*cancel c^7)#

#rArr (b^2*c)/1#

Hence the answer is

#color(blue)(b^2c)#

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Answer 2

Caleb Alexander

To simplify the expression ( \frac { b ^ { 2} c ^ { 8} } { b c ^ { 0} \cdot b ^ { - 1} c ^ { 7} } ), use the properties of exponents. Recall that ( a^{0} = 1 ) for any ( a \neq 0 ). Also, ( a^{-n} = \frac{1}{a^n} ). Applying these rules, simplify the expression to get ( b^{2-1} \cdot c^{8-0-7} ), which simplifies to ( b \cdot c^1 ), or just ( bc ).

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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.