Solve (6x^{6}y^8)^-3(7x^3y^4)

$$( 6 x ^ { 6 } y ^ { 8 } ) ^ { - 3 } ( 7 x ^ { 3 } y ^ { 4 } )$$

Evaluate

$$\frac{7}{216x^{15}y^{20}}$$

Solution Steps

Expand \left(6x^{6}y^{8}\right)^{-3}.

$$6^{-3}\left(x^{6}\right)^{-3}\left(y^{8}\right)^{-3}\times 7x^{3}y^{4}$$

To raise a power to another power, multiply the exponents. Multiply 6 and -3 to get -18.

$$6^{-3}x^{-18}\left(y^{8}\right)^{-3}\times 7x^{3}y^{4}$$

To raise a power to another power, multiply the exponents. Multiply 8 and -3 to get -24.

$$6^{-3}x^{-18}y^{-24}\times 7x^{3}y^{4}$$

Calculate 6 to the power of -3 and get \frac{1}{216}.

$$\frac{1}{216}x^{-18}y^{-24}\times 7x^{3}y^{4}$$

Multiply \frac{1}{216} and 7 to get \frac{7}{216}.

$$\frac{7}{216}x^{-18}y^{-24}x^{3}y^{4}$$

To multiply powers of the same base, add their exponents. Add -18 and 3 to get -15.

$$\frac{7}{216}x^{-15}y^{-24}y^{4}$$

To multiply powers of the same base, add their exponents. Add -24 and 4 to get -20.

$$\frac{7}{216}x^{-15}y^{-20}$$

Expand

$$\frac{7}{216x^{15}y^{20}}$$

Solution Steps

Expand \left(6x^{6}y^{8}\right)^{-3}.

$$6^{-3}\left(x^{6}\right)^{-3}\left(y^{8}\right)^{-3}\times 7x^{3}y^{4}$$

To raise a power to another power, multiply the exponents. Multiply 6 and -3 to get -18.

$$6^{-3}x^{-18}\left(y^{8}\right)^{-3}\times 7x^{3}y^{4}$$

To raise a power to another power, multiply the exponents. Multiply 8 and -3 to get -24.

$$6^{-3}x^{-18}y^{-24}\times 7x^{3}y^{4}$$

Calculate 6 to the power of -3 and get \frac{1}{216}.

$$\frac{1}{216}x^{-18}y^{-24}\times 7x^{3}y^{4}$$

Multiply \frac{1}{216} and 7 to get \frac{7}{216}.

$$\frac{7}{216}x^{-18}y^{-24}x^{3}y^{4}$$

To multiply powers of the same base, add their exponents. Add -18 and 3 to get -15.

$$\frac{7}{216}x^{-15}y^{-24}y^{4}$$

To multiply powers of the same base, add their exponents. Add -24 and 4 to get -20.

$$\frac{7}{216}x^{-15}y^{-20}$$