Solve 7^2*4sqrt{5}div7/4left(x^2right)^7=

$${ 7 }^{ 2 } \times 4 \sqrt{ 5 } \div \frac{ 7 }{ 4 } { \left( { x }^{ 2 } \right) }^{ 7 } =$$

Evaluate

$$112\sqrt{5}x^{14}$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 2 and 7 to get 14.

$$\frac{4\times 7^{2}\sqrt{5}}{\frac{7}{4}}x^{14}$$

Calculate 7 to the power of 2 and get 49.

$$\frac{4\times 49\sqrt{5}}{\frac{7}{4}}x^{14}$$

Multiply 4 and 49 to get 196.

$$\frac{196\sqrt{5}}{\frac{7}{4}}x^{14}$$

Divide 196\sqrt{5} by \frac{7}{4} by multiplying 196\sqrt{5} by the reciprocal of \frac{7}{4}.

$$\frac{196\sqrt{5}\times 4}{7}x^{14}$$

Multiply 196 and 4 to get 784.

$$\frac{784\sqrt{5}}{7}x^{14}$$

Divide 784\sqrt{5} by 7 to get 112\sqrt{5}.

$$112\sqrt{5}x^{14}$$

Differentiate w.r.t. x

$$1568\sqrt{5}x^{13}$$