Solve (4x^{6}y^5)^-2(6x^4y^3)

$$( 4 x ^ { 6 } y ^ { 5 } ) ^ { - 2 } ( 6 x ^ { 4 } y ^ { 3 } )$$

Evaluate

$$\frac{3}{8y^{7}x^{8}}$$

Solution Steps

Expand \left(4x^{6}y^{5}\right)^{-2}.

$$4^{-2}\left(x^{6}\right)^{-2}\left(y^{5}\right)^{-2}\times 6x^{4}y^{3}$$

To raise a power to another power, multiply the exponents. Multiply 6 and -2 to get -12.

$$4^{-2}x^{-12}\left(y^{5}\right)^{-2}\times 6x^{4}y^{3}$$

To raise a power to another power, multiply the exponents. Multiply 5 and -2 to get -10.

$$4^{-2}x^{-12}y^{-10}\times 6x^{4}y^{3}$$

Calculate 4 to the power of -2 and get \frac{1}{16}.

$$\frac{1}{16}x^{-12}y^{-10}\times 6x^{4}y^{3}$$

Multiply \frac{1}{16} and 6 to get \frac{3}{8}.

$$\frac{3}{8}x^{-12}y^{-10}x^{4}y^{3}$$

To multiply powers of the same base, add their exponents. Add -12 and 4 to get -8.

$$\frac{3}{8}x^{-8}y^{-10}y^{3}$$

To multiply powers of the same base, add their exponents. Add -10 and 3 to get -7.

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

Expand

$$\frac{3}{8y^{7}x^{8}}$$

Solution Steps

Expand \left(4x^{6}y^{5}\right)^{-2}.

$$4^{-2}\left(x^{6}\right)^{-2}\left(y^{5}\right)^{-2}\times 6x^{4}y^{3}$$

To raise a power to another power, multiply the exponents. Multiply 6 and -2 to get -12.

$$4^{-2}x^{-12}\left(y^{5}\right)^{-2}\times 6x^{4}y^{3}$$

To raise a power to another power, multiply the exponents. Multiply 5 and -2 to get -10.

$$4^{-2}x^{-12}y^{-10}\times 6x^{4}y^{3}$$

Calculate 4 to the power of -2 and get \frac{1}{16}.

$$\frac{1}{16}x^{-12}y^{-10}\times 6x^{4}y^{3}$$

Multiply \frac{1}{16} and 6 to get \frac{3}{8}.

$$\frac{3}{8}x^{-12}y^{-10}x^{4}y^{3}$$

To multiply powers of the same base, add their exponents. Add -12 and 4 to get -8.

$$\frac{3}{8}x^{-8}y^{-10}y^{3}$$

To multiply powers of the same base, add their exponents. Add -10 and 3 to get -7.

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