Solve frac{p^{0}q^{0}rs}{p^{-1}q^{-9}r^{0}s^6*pq^0r^-8s^-1}

$$\frac { p ^ { 0 } q ^ { 0 } r s } { p ^ { - 1 } q ^ { - 9 } r ^ { 0 } s ^ { 6 } \cdot p q ^ { 0 } r ^ { - 8 } s ^ { - 1 } }$$

Evaluate

$$\frac{\left(qr\right)^{9}}{s^{4}}$$

Short Solution Steps

Multiply p^{-1} and p to get 1.

$$\frac{p^{0}q^{0}rs}{q^{-9}r^{0}s^{6}q^{0}r^{-8}s^{-1}}$$

To multiply powers of the same base, add their exponents. Add -9 and 0 to get -9.

$$\frac{p^{0}q^{0}rs}{q^{-9}r^{0}s^{6}r^{-8}s^{-1}}$$

To multiply powers of the same base, add their exponents. Add 0 and -8 to get -8.

$$\frac{p^{0}q^{0}rs}{q^{-9}r^{-8}s^{6}s^{-1}}$$

To multiply powers of the same base, add their exponents. Add 6 and -1 to get 5.

$$\frac{p^{0}q^{0}rs}{q^{-9}r^{-8}s^{5}}$$

Cancel out s in both numerator and denominator.

$$\frac{rp^{0}q^{0}}{q^{-9}r^{-8}s^{4}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$\frac{p^{0}q^{9}r^{9}}{s^{4}}$$

Calculate p to the power of 0 and get 1.

$$\frac{1q^{9}r^{9}}{s^{4}}$$

For any term t, t\times 1=t and 1t=t.

$$\frac{q^{9}r^{9}}{s^{4}}$$

Differentiate w.r.t. s

$$-\frac{4\left(qr\right)^{9}}{s^{5}}$$