Solve 6(27)^2/3(16)^1/4*(27)^-1(16)^1/2

$$6 ( 27 ) ^ { 2 / 3 } ( 16 ) ^ { 1 / 4 } \cdot ( 27 ) ^ { - 1 } ( 16 ) ^ { 1 / 2 }$$

Evaluate

$$16$$

Solution Steps

To multiply powers of the same base, add their exponents. Add \frac{2}{3} and -1 to get -\frac{1}{3}.

$$6\times 27^{-\frac{1}{3}}\times 16^{\frac{1}{4}}\times 16^{\frac{1}{2}}$$

To multiply powers of the same base, add their exponents. Add \frac{1}{4} and \frac{1}{2} to get \frac{3}{4}.

$$6\times 27^{-\frac{1}{3}}\times 16^{\frac{3}{4}}$$

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

$$6\times \frac{1}{3}\times 16^{\frac{3}{4}}$$

Multiply 6 and \frac{1}{3} to get 2.

$$2\times 16^{\frac{3}{4}}$$

Calculate 16 to the power of \frac{3}{4} and get 8.

$$2\times 8$$

Multiply 2 and 8 to get 16.

$$16$$

Factor

$$2^{4}$$