How do you simplify #a^5/(b^3c^3) div a^4/(b^3c^4)#?

Answer 1

You cancel terms common to the numerator and denominator.

Your expression can be written as

#(a^5)/(b^3c^3) * (b^3c^4)/a^4#

Use the product of powers property of exponents to rewrite the numerators of the two fractions as

#a^5 = a^4 * a#
#b^3 c^4 = b^3c^3 * c#

Your expression will become

#(a^4 * a)/(b^3c^3) * (b^3c^3 * c)/a^4#

Cancel the terms common to the numerator and denominator to get

#(color(red)(cancel(color(black)(a^4))) * a)/(color(blue)(cancel(color(black)(b^3c^3)))) * (color(blue)(cancel(color(black)(b^3c^3))) * c)/(color(red)(cancel(color(black)(a^4)))) = color(green)(ac)#
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Answer 2

To simplify the expression (a^5/(b^3c^3)) ÷ (a^4/(b^3c^4)), we can use the division rule of exponents. When dividing two terms with the same base, we subtract the exponents.

In this case, the base is 'a', and the exponents are 5 and 4. Subtracting 4 from 5 gives us a^1.

For the variable 'b', the exponents are both 3, so we subtract 3 from 3, resulting in b^0. Any term with an exponent of 0 is equal to 1.

Lastly, for the variable 'c', we subtract 3 from 4, giving us c^1.

Therefore, the simplified expression is a^1/(b^0c^1), which can be further simplified to a/(c).

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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.

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.

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.

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.

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