Solve [(125)^2*8/(64)^38]^frac{1{3}}

$$[ \frac { ( 125 ) ^ { 2 } \times 8 } { ( 64 ) ^ { 38 } } ] ^ { \frac { 1 } { 3 } }$$

Evaluate

$$\frac{25}{37778931862957161709568}=6.6174449 \cdot 10^{-22}$$

Solution Steps

Calculate 125 to the power of 2 and get 15625.

$$\left(\frac{15625\times 8}{64^{38}}\right)^{\frac{1}{3}}$$

Multiply 15625 and 8 to get 125000.

$$\left(\frac{125000}{64^{38}}\right)^{\frac{1}{3}}$$

Calculate 64 to the power of 38 and get 431359146674410236714672241392314090778194310760649159697657763987456.

$$\left(\frac{125000}{431359146674410236714672241392314090778194310760649159697657763987456}\right)^{\frac{1}{3}}$$

Reduce the fraction \frac{125000}{431359146674410236714672241392314090778194310760649159697657763987456} to lowest terms by extracting and canceling out 8.

$$\left(\frac{15625}{53919893334301279589334030174039261347274288845081144962207220498432}\right)^{\frac{1}{3}}$$

Calculate \frac{15625}{53919893334301279589334030174039261347274288845081144962207220498432} to the power of \frac{1}{3} and get \frac{25}{37778931862957161709568}.

$$\frac{25}{37778931862957161709568}$$

Factor

$$\frac{5 ^ {2}}{2 ^ {75}} = 6.617444900424221 \times 10^{-22}$$