Solve frac{5^{-2}b^{7}c^4}{4^-3b^2c^8}

$$\frac { 5 ^ { - 2 } b ^ { 7 } c ^ { 4 } } { 4 ^ { - 3 } b ^ { 2 } c ^ { 8 } }$$

Evaluate

$$\frac{64b^{5}}{25c^{4}}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{5^{-2}b^{7}c^{4}}{4^{-3}b^{2}c^{8}}$$

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

$$\frac{5^{-2}}{4^{-3}}b^{7-2}c^{4-8}$$

Subtract 2 from 7.

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

Subtract 8 from 4.

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

Divide \frac{1}{25} by \frac{1}{64} by multiplying \frac{1}{25} by the reciprocal of \frac{1}{64}.

$$\frac{64}{25}b^{5}\times \frac{1}{c^{4}}$$

Differentiate w.r.t. c

$$-\frac{256\times \left(\frac{b}{c}\right)^{5}}{25}$$