Solve frac{4^{2}a^4b^2}{2^3ab^5}

$$\frac { 4 ^ { 2 } a ^ { 4 } b ^ { 2 } } { 2 ^ { 3 } a b ^ { 5 } }$$

Evaluate

$$2\times \left(\frac{a}{b}\right)^{3}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{4^{2}a^{4}b^{2}}{2^{3}a^{1}b^{5}}$$

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

$$\frac{4^{2}}{2^{3}}a^{4-1}b^{2-5}$$

Subtract 1 from 4.

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

Subtract 5 from 2.

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

Divide 16 by 8.

$$2a^{3}\times \frac{1}{b^{3}}$$

Differentiate w.r.t. b

$$-\frac{6a^{3}}{b^{4}}$$