Solve (5x^-8y^4)(5x^-3y^6)

$$(5 { x }^{ -8 } { y }^{ 4 } )(5 { x }^{ -3 } { y }^{ 6 } )$$

Evaluate

$$\frac{25y^{10}}{x^{11}}$$

Steps Using Commutative Property of Multiplication

Use the rules of exponents to simplify the expression.

$$5^{1}x^{-8}y^{4}\times 5^{1}x^{-3}y^{6}$$

Use the Commutative Property of Multiplication.

$$5^{1}\times 5^{1}x^{-8}x^{-3}y^{4}y^{6}$$

To multiply powers of the same base, add their exponents.

$$5^{1+1}x^{-8-3}y^{4+6}$$

Add the exponents 1 and 1.

$$5^{2}x^{-8-3}y^{4+6}$$

Raise 5 to the power 2.

$$25x^{-8-3}y^{4+6}$$

Add the exponents -8 and -3.

$$25x^{-11}y^{4+6}$$

Add the exponents 4 and 6.

$$25\times \frac{1}{x^{11}}y^{10}$$

Differentiate w.r.t. x

$$-\frac{275y^{10}}{x^{12}}$$