Solve frac{7a^{-4}b^4}{28a^-3b^-3}28a/7a^4

$$\frac { 7 a ^ { - 4 } b ^ { 4 } } { 28 a ^ { - 3 } b ^ { - 3 } } \frac { 28 a } { 7 a ^ { 4 } }$$

Evaluate

$$\frac{b^{7}}{a^{4}}$$

Solution Steps

Cancel out 7 in both numerator and denominator.

$$\frac{a^{-4}b^{4}}{4a^{-3}b^{-3}}\times \frac{28a}{7a^{4}}$$

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

$$\frac{a^{-4}b^{7}}{4a^{-3}}\times \frac{28a}{7a^{4}}$$

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

$$\frac{b^{7}}{4a^{1}}\times \frac{28a}{7a^{4}}$$

Calculate a to the power of 1 and get a.

$$\frac{b^{7}}{4a}\times \frac{28a}{7a^{4}}$$

Cancel out 7a in both numerator and denominator.

$$\frac{b^{7}}{4a}\times \frac{4}{a^{3}}$$

Multiply \frac{b^{7}}{4a} times \frac{4}{a^{3}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{b^{7}\times 4}{4aa^{3}}$$

Cancel out 4 in both numerator and denominator.

$$\frac{b^{7}}{aa^{3}}$$

To multiply powers of the same base, add their exponents. Add 1 and 3 to get 4.

$$\frac{b^{7}}{a^{4}}$$

Differentiate w.r.t. b

$$\frac{7b^{6}}{a^{4}}$$