Solve frac{(3^{7}*a^8b^3)}{(9*a^5b^2)}

$$\frac { ( 3 ^ { 7 } \times a ^ { 8 } b ^ { 3 } ) } { ( 9 \times a ^ { 5 } b ^ { 2 } ) }$$

Evaluate

$$243ba^{3}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{3^{7}a^{8}b^{3}}{9^{1}a^{5}b^{2}}$$

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

$$\frac{3^{7}}{9^{1}}a^{8-5}b^{3-2}$$

Subtract 5 from 8.

$$\frac{3^{7}}{9^{1}}a^{3}b^{3-2}$$

Subtract 2 from 3.

$$\frac{3^{7}}{9^{1}}a^{3}b^{1}$$

Divide 2187 by 9.

$$243a^{3}b$$

Differentiate w.r.t. b

$$243a^{3}$$