Solve (16x^-4)^-frac{1{2}}div(8x^6)^frac{1{3}}

$$( 16 x ^ { - 4 } ) ^ { - \frac { 1 } { 2 } } \div ( 8 x ^ { 6 } ) ^ { \frac { 1 } { 3 } }$$

Evaluate

$$\frac{1}{8}=0.125$$

Solution Steps

Expand \left(16x^{-4}\right)^{-\frac{1}{2}}.

$$\frac{16^{-\frac{1}{2}}\left(x^{-4}\right)^{-\frac{1}{2}}}{\left(8x^{6}\right)^{\frac{1}{3}}}$$

To raise a power to another power, multiply the exponents. Multiply -4 and -\frac{1}{2} to get 2.

$$\frac{16^{-\frac{1}{2}}x^{2}}{\left(8x^{6}\right)^{\frac{1}{3}}}$$

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

$$\frac{\frac{1}{4}x^{2}}{\left(8x^{6}\right)^{\frac{1}{3}}}$$

Expand \left(8x^{6}\right)^{\frac{1}{3}}.

$$\frac{\frac{1}{4}x^{2}}{8^{\frac{1}{3}}\left(x^{6}\right)^{\frac{1}{3}}}$$

To raise a power to another power, multiply the exponents. Multiply 6 and \frac{1}{3} to get 2.

$$\frac{\frac{1}{4}x^{2}}{8^{\frac{1}{3}}x^{2}}$$

Calculate 8 to the power of \frac{1}{3} and get 2.

$$\frac{\frac{1}{4}x^{2}}{2x^{2}}$$

Cancel out x^{2} in both numerator and denominator.

$$\frac{\frac{1}{4}}{2}$$

Express \frac{\frac{1}{4}}{2} as a single fraction.

$$\frac{1}{4\times 2}$$

Multiply 4 and 2 to get 8.

$$\frac{1}{8}$$

Factor

$$\frac{1}{2 ^ {3}} = 0.125$$