Solve (3^5div3^8)^3*3^-4

$$( 3 ^ { 5 } \div 3 ^ { 8 } ) ^ { 3 } \times 3 ^ { - 4 }$$

Evaluate

$$\frac{1}{1594323}\approx 0.000000627$$

Solution Steps

Rewrite 3^{8} as 3^{5}\times 3^{3}. Cancel out 3^{5} in both numerator and denominator.

$$\left(\frac{1}{3^{3}}\right)^{3}\times 3^{-4}$$

Calculate 3 to the power of 3 and get 27.

$$\left(\frac{1}{27}\right)^{3}\times 3^{-4}$$

Calculate \frac{1}{27} to the power of 3 and get \frac{1}{19683}.

$$\frac{1}{19683}\times 3^{-4}$$

Calculate 3 to the power of -4 and get \frac{1}{81}.

$$\frac{1}{19683}\times \frac{1}{81}$$

Multiply \frac{1}{19683} and \frac{1}{81} to get \frac{1}{1594323}.

$$\frac{1}{1594323}$$

Factor

$$\frac{1}{3 ^ {13}} = 6.27225474386307 \times 10^{-7}$$