Solve 6^-45^-72^6/2^-5{6^-6}

$$\frac{ { 6 }^{ -4 } { 5 }^{ -7 } { 2 }^{ 6 } }{ { 2 }^{ -5 } { 6 }^{ -6 } }$$

Evaluate

$$\frac{73728}{78125}=0.9437184$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$2^{11}\times 5^{-7}\times 6^{2}$$

Calculate 2 to the power of 11 and get 2048.

$$2048\times 5^{-7}\times 6^{2}$$

Calculate 5 to the power of -7 and get \frac{1}{78125}.

$$2048\times \frac{1}{78125}\times 6^{2}$$

Multiply 2048 and \frac{1}{78125} to get \frac{2048}{78125}.

$$\frac{2048}{78125}\times 6^{2}$$

Calculate 6 to the power of 2 and get 36.

$$\frac{2048}{78125}\times 36$$

Multiply \frac{2048}{78125} and 36 to get \frac{73728}{78125}.

$$\frac{73728}{78125}$$

Factor

$$\frac{2 ^ {13} \cdot 3 ^ {2}}{5 ^ {7}} = 0.9437184$$