Solve (25^3x^-2)(1/4y^7x)(16x^4)

$$( { 25 }^{ 3 } { x }^{ -2 } )( \frac{ 1 }{ 4 } { y }^{ 7 } x)(16 { x }^{ 4 } )$$

Evaluate

$$62500x^{3}y^{7}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add -2 and 1 to get -1.

$$25^{3}x^{-1}\times \frac{1}{4}y^{7}\times 16x^{4}$$

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

$$25^{3}x^{3}\times \frac{1}{4}y^{7}\times 16$$

Calculate 25 to the power of 3 and get 15625.

$$15625x^{3}\times \frac{1}{4}y^{7}\times 16$$

Multiply 15625 and \frac{1}{4} to get \frac{15625}{4}.

$$\frac{15625}{4}x^{3}y^{7}\times 16$$

Multiply \frac{15625}{4} and 16 to get 62500.

$$62500x^{3}y^{7}$$

Differentiate w.r.t. x

$$187500x^{2}y^{7}$$