Solve (5x^{5}y^2)^-4(6x^7y^6)

$$( 5 x ^ { 5 } y ^ { 2 } ) ^ { - 4 } ( 6 x ^ { 7 } y ^ { 6 } )$$

Evaluate

$$\frac{6}{625y^{2}x^{13}}$$

Solution Steps

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

$$5^{-4}\left(x^{5}\right)^{-4}\left(y^{2}\right)^{-4}\times 6x^{7}y^{6}$$

To raise a power to another power, multiply the exponents. Multiply 5 and -4 to get -20.

$$5^{-4}x^{-20}\left(y^{2}\right)^{-4}\times 6x^{7}y^{6}$$

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

$$5^{-4}x^{-20}y^{-8}\times 6x^{7}y^{6}$$

Calculate 5 to the power of -4 and get \frac{1}{625}.

$$\frac{1}{625}x^{-20}y^{-8}\times 6x^{7}y^{6}$$

Multiply \frac{1}{625} and 6 to get \frac{6}{625}.

$$\frac{6}{625}x^{-20}y^{-8}x^{7}y^{6}$$

To multiply powers of the same base, add their exponents. Add -20 and 7 to get -13.

$$\frac{6}{625}x^{-13}y^{-8}y^{6}$$

To multiply powers of the same base, add their exponents. Add -8 and 6 to get -2.

$$\frac{6}{625}x^{-13}y^{-2}$$

Expand

$$\frac{6}{625y^{2}x^{13}}$$

Solution Steps

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

$$5^{-4}\left(x^{5}\right)^{-4}\left(y^{2}\right)^{-4}\times 6x^{7}y^{6}$$

To raise a power to another power, multiply the exponents. Multiply 5 and -4 to get -20.

$$5^{-4}x^{-20}\left(y^{2}\right)^{-4}\times 6x^{7}y^{6}$$

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

$$5^{-4}x^{-20}y^{-8}\times 6x^{7}y^{6}$$

Calculate 5 to the power of -4 and get \frac{1}{625}.

$$\frac{1}{625}x^{-20}y^{-8}\times 6x^{7}y^{6}$$

Multiply \frac{1}{625} and 6 to get \frac{6}{625}.

$$\frac{6}{625}x^{-20}y^{-8}x^{7}y^{6}$$

To multiply powers of the same base, add their exponents. Add -20 and 7 to get -13.

$$\frac{6}{625}x^{-13}y^{-8}y^{6}$$

To multiply powers of the same base, add their exponents. Add -8 and 6 to get -2.

$$\frac{6}{625}x^{-13}y^{-2}$$