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How do you simplify #x^(n+2) div x^(n-3)#?

Answer 1

Genesis Allen

#x^5#

#color(blue)(x^(n+2)-:x^(n-3)#

Remember the law of exponents #color(brown)(x^y-:x^z=x^(y-z)#

#:.x^(n+2)-:x^(n-3)=x^((n+2)-(n-3))#

#rarrx^(n+2-n+3)#

Gather up the like terms

#rarrx^((n-n)+2+3)#

#rarrx^(2+3)#

#color(green)(rArrx^5#

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Answer 2

Ethan Adkins

To simplify ( \frac{x^{n+2}}{x^{n-3}} ), you subtract the exponents since the bases are the same. Therefore, ( x^{n+2} \div x^{n-3} = x^{(n+2) - (n-3)} = x^{n+2 - n + 3} = x^5 ).

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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.