Solve frac{3^{-2}z^{-5}b^2}{2^-2z^-8b^-4}

$$\frac { 3 ^ { - 2 } z ^ { - 5 } b ^ { 2 } } { 2 ^ { - 2 } z ^ { - 8 } b ^ { - 4 } }$$

Evaluate

$$\frac{4z^{3}b^{6}}{9}$$

Solution Steps

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

$$\frac{3^{-2}z^{3}b^{6}}{2^{-2}}$$

Calculate 3 to the power of -2 and get \frac{1}{9}.

$$\frac{\frac{1}{9}z^{3}b^{6}}{2^{-2}}$$

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

$$\frac{\frac{1}{9}z^{3}b^{6}}{\frac{1}{4}}$$

Divide \frac{1}{9}z^{3}b^{6} by \frac{1}{4} by multiplying \frac{1}{9}z^{3}b^{6} by the reciprocal of \frac{1}{4}.

$$\frac{1}{9}z^{3}b^{6}\times 4$$

Multiply \frac{1}{9} and 4 to get \frac{4}{9}.

$$\frac{4}{9}z^{3}b^{6}$$

Differentiate w.r.t. b

$$\frac{8z^{3}b^{5}}{3}$$