Solve (5x^{4}y^3)^-2(y^7x^-3)

$$( 5 x ^ { 4 } y ^ { 3 } ) ^ { - 2 } ( y ^ { 7 } x ^ { - 3 } )$$

Evaluate

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

Solution Steps

Expand \left(5x^{4}y^{3}\right)^{-2}.

$$5^{-2}\left(x^{4}\right)^{-2}\left(y^{3}\right)^{-2}y^{7}x^{-3}$$

To raise a power to another power, multiply the exponents. Multiply 4 and -2 to get -8.

$$5^{-2}x^{-8}\left(y^{3}\right)^{-2}y^{7}x^{-3}$$

To raise a power to another power, multiply the exponents. Multiply 3 and -2 to get -6.

$$5^{-2}x^{-8}y^{-6}y^{7}x^{-3}$$

Calculate 5 to the power of -2 and get \frac{1}{25}.

$$\frac{1}{25}x^{-8}y^{-6}y^{7}x^{-3}$$

To multiply powers of the same base, add their exponents. Add -6 and 7 to get 1.

$$\frac{1}{25}x^{-8}y^{1}x^{-3}$$

To multiply powers of the same base, add their exponents. Add -8 and -3 to get -11.

$$\frac{1}{25}x^{-11}y^{1}$$

Calculate y to the power of 1 and get y.

$$\frac{1}{25}x^{-11}y$$

Expand

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

Solution Steps

Expand \left(5x^{4}y^{3}\right)^{-2}.

$$5^{-2}\left(x^{4}\right)^{-2}\left(y^{3}\right)^{-2}y^{7}x^{-3}$$

To raise a power to another power, multiply the exponents. Multiply 4 and -2 to get -8.

$$5^{-2}x^{-8}\left(y^{3}\right)^{-2}y^{7}x^{-3}$$

To raise a power to another power, multiply the exponents. Multiply 3 and -2 to get -6.

$$5^{-2}x^{-8}y^{-6}y^{7}x^{-3}$$

Calculate 5 to the power of -2 and get \frac{1}{25}.

$$\frac{1}{25}x^{-8}y^{-6}y^{7}x^{-3}$$

To multiply powers of the same base, add their exponents. Add -6 and 7 to get 1.

$$\frac{1}{25}x^{-8}y^{1}x^{-3}$$

To multiply powers of the same base, add their exponents. Add -8 and -3 to get -11.

$$\frac{1}{25}x^{-11}y^{1}$$

Calculate y to the power of 1 and get y.

$$\frac{1}{25}x^{-11}y$$