Solve frac{8a^{-4}b^6}{2^-1a^7b^-6}

$$\frac { 8 a ^ { - 4 } b ^ { 6 } } { 2 ^ { - 1 } a ^ { 7 } b ^ { - 6 } }$$

Evaluate

$$\frac{16b^{12}}{a^{11}}$$

Solution Steps

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

$$\frac{8a^{-4}b^{12}}{\frac{1}{2}a^{7}}$$

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

$$\frac{8b^{12}}{\frac{1}{2}a^{11}}$$

Differentiate w.r.t. a

$$-176\times \left(\frac{b}{a}\right)^{12}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{8b^{6}\times 2b^{6}}{1}a^{-4-7})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}a}(16b^{12}a^{-11})$$

The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of ax^{n} is nax^{n-1}.

$$-11\times 16b^{12}a^{-11-1}$$

Do the arithmetic.

$$\left(-176b^{12}\right)a^{-12}$$