Solve frac{2^{-3}a^-1b^-2}{4^-2a^-2b}

$$\frac { 2 ^ { - 3 } a ^ { - 1 } b ^ { - 2 } } { 4 ^ { - 2 } a ^ { - 2 } b }$$

Evaluate

$$\frac{2a}{b^{3}}$$

Solution Steps

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

$$\frac{2^{-3}b^{-2}a^{1}}{4^{-2}b}$$

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

$$\frac{2^{-3}a^{1}}{4^{-2}b^{3}}$$

Calculate 2 to the power of -3 and get \frac{1}{8}.

$$\frac{\frac{1}{8}a^{1}}{4^{-2}b^{3}}$$

Calculate a to the power of 1 and get a.

$$\frac{\frac{1}{8}a}{4^{-2}b^{3}}$$

Calculate 4 to the power of -2 and get \frac{1}{16}.

$$\frac{\frac{1}{8}a}{\frac{1}{16}b^{3}}$$

Differentiate w.r.t. b

$$-\frac{6a}{b^{4}}$$