Solve x^6(x^6bc)^-8

$$x ^ { 6 } ( x ^ { 6 } b c ) ^ { - 8 }$$

Evaluate

$$\frac{1}{\left(bc\right)^{8}x^{42}}$$

Solution Steps

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

$$x^{6}\left(x^{6}\right)^{-8}b^{-8}c^{-8}$$

To raise a power to another power, multiply the exponents. Multiply 6 and -8 to get -48.

$$x^{6}x^{-48}b^{-8}c^{-8}$$

To multiply powers of the same base, add their exponents. Add 6 and -48 to get -42.

$$x^{-42}b^{-8}c^{-8}$$

Expand

$$\frac{1}{\left(bc\right)^{8}x^{42}}$$

Solution Steps

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

$$x^{6}\left(x^{6}\right)^{-8}b^{-8}c^{-8}$$

To raise a power to another power, multiply the exponents. Multiply 6 and -8 to get -48.

$$x^{6}x^{-48}b^{-8}c^{-8}$$

To multiply powers of the same base, add their exponents. Add 6 and -48 to get -42.

$$x^{-42}b^{-8}c^{-8}$$