Solve {left(lceil{243}^frac{-4{5}}{64}^frac{2{3}}rceilright)}^frac{1{4}}

$${ \left( \lceil { 243 }^{ \frac{ -4 }{ 5 } } { 64 }^{ \frac{ 2 }{ 3 } } \rceil \right) }^{ \frac{ 1 }{ 4 } }$$

Evaluate

$$1$$

Solution Steps

Fraction \frac{-4}{5} can be rewritten as -\frac{4}{5} by extracting the negative sign.

$$\left(\lceil 243^{-\frac{4}{5}}\times 64^{\frac{2}{3}}\rceil \right)^{\frac{1}{4}}$$

Calculate 243 to the power of -\frac{4}{5} and get \frac{1}{81}.

$$\left(\lceil \frac{1}{81}\times 64^{\frac{2}{3}}\rceil \right)^{\frac{1}{4}}$$

Calculate 64 to the power of \frac{2}{3} and get 16.

$$\left(\lceil \frac{1}{81}\times 16\rceil \right)^{\frac{1}{4}}$$

Multiply \frac{1}{81} and 16 to get \frac{16}{81}.

$$\left(\lceil \frac{16}{81}\rceil \right)^{\frac{1}{4}}$$

Dividing 16 by 81 gives 0 and remainder 16. Rewrite \frac{16}{81} as 0+\frac{16}{81}.

$$\left(\lceil 0+\frac{16}{81}\rceil \right)^{\frac{1}{4}}$$

The ceiling of a real number a is the smallest integer number greater than or equal to a. The ceiling of 0+\frac{16}{81} is 1.

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

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

$$1$$

Factor

$$1$$