# How do you simplify #(2p^3q^2)/(8p^4q) div (4pq^2)/(16p^4)#?

We start off with what's given:

So,

So,

So, our original setup was:

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The answer is

Reduce the numerical part of each fraction.

Simplify each fraction.

In order to divide fractions, invert the second fraction to get its reciprocal, and then multiply.

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To simplify the expression (2p^3q^2)/(8p^4q) ÷ (4pq^2)/(16p^4), we can follow these steps:

- Rewrite the division as multiplication by taking the reciprocal of the second fraction: (2p^3q^2)/(8p^4q) × (16p^4)/(4pq^2).
- Simplify the numerator by multiplying the coefficients and combining the variables with the same base: (2 × 16) × (p^3 × p^4) × (q^2)/(8 × 4 × p^4 × q × q^2).
- Simplify the denominator by multiplying the coefficients and combining the variables with the same base: (2 × 16) × (p^3 × p^4) × (q^2)/(8 × 4 × p^4 × q × q^2).
- Cancel out common factors between the numerator and denominator: (2 × 16)/(8 × 4) × (p^3 × p^4)/(p^4) × (q^2)/(q × q^2).
- Simplify the remaining expression: 32/32 × p^(3+4)/p^4 × q^(2-1)/q^2.
- Further simplify the expression: 1 × p^7/p^4 × q/q^2.
- Combine the variables with the same base by subtracting the exponents: p^(7-4) × q^(1-2).
- Simplify the exponents: p^3/q.
- The simplified expression is (p^3)/q.

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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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