Solve 4^1/2(27^-1/3)^8

$$4 ^ { 1 / 2 } ( 27 ^ { - 1 / 3 } ) ^ { 8 }$$

Evaluate

$$\frac{2}{6561}\approx 0.000304832$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply -\frac{1}{3} and 8 to get -\frac{8}{3}.

$$4^{\frac{1}{2}}\times 27^{-\frac{8}{3}}$$

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

$$2\times 27^{-\frac{8}{3}}$$

Calculate 27 to the power of -\frac{8}{3} and get \frac{1}{6561}.

$$2\times \frac{1}{6561}$$

Multiply 2 and \frac{1}{6561} to get \frac{2}{6561}.

$$\frac{2}{6561}$$

Factor

$$\frac{2}{3 ^ {8}} = 0.00030483158055174517$$