Solve {l}{(-3)(-3)(-3)}{[frac{(-3)^{6}(-30)^{4}(-32)^{3}(-4)^{2}}{(-4)^15(-4)^2(-30)^-6}]^4}

$$\left. \begin{array} { l } { ( - 3 ) ( - 3 ) ( - 3 ) } \\ { [ \frac { ( - 3 ) ^ { 6 } ( - 30 ) ^ { 4 } ( - 32 ) ^ { 3 } ( - 4 ) ^ { 2 } } { ( - 4 ) ^ { 15 } ( - 4 ) ^ { 2 } ( - 30 ) ^ { - 6 } } ] ^ { 4 } } \end{array} \right.$$

Sort

$$-27,\ \frac{31229172421194675595487288676677053445018827915191650390625}{1048576}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 15 and 2 to get 17.

$$sort(-3\left(-3\right)\left(-3\right),\left(\frac{\left(-3\right)^{6}\left(-30\right)^{4}\left(-32\right)^{3}\left(-4\right)^{2}}{\left(-4\right)^{17}\left(-30\right)^{-6}}\right)^{4})$$

Multiply -3 and -3 to get 9.

$$sort(9\left(-3\right),\left(\frac{\left(-3\right)^{6}\left(-30\right)^{4}\left(-32\right)^{3}\left(-4\right)^{2}}{\left(-4\right)^{17}\left(-30\right)^{-6}}\right)^{4})$$

Multiply 9 and -3 to get -27.

$$sort(-27,\left(\frac{\left(-3\right)^{6}\left(-30\right)^{4}\left(-32\right)^{3}\left(-4\right)^{2}}{\left(-4\right)^{17}\left(-30\right)^{-6}}\right)^{4})$$

Cancel out \left(-4\right)^{2} in both numerator and denominator.

$$sort(-27,\left(\frac{\left(-32\right)^{3}\left(-30\right)^{4}\left(-3\right)^{6}}{\left(-30\right)^{-6}\left(-4\right)^{15}}\right)^{4})$$

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

$$sort(-27,\left(\frac{\left(-32\right)^{3}\left(-30\right)^{10}\left(-3\right)^{6}}{\left(-4\right)^{15}}\right)^{4})$$

Calculate -32 to the power of 3 and get -32768.

$$sort(-27,\left(\frac{-32768\left(-30\right)^{10}\left(-3\right)^{6}}{\left(-4\right)^{15}}\right)^{4})$$

Calculate -30 to the power of 10 and get 590490000000000.

$$sort(-27,\left(\frac{-32768\times 590490000000000\left(-3\right)^{6}}{\left(-4\right)^{15}}\right)^{4})$$

Multiply -32768 and 590490000000000 to get -19349176320000000000.

$$sort(-27,\left(\frac{-19349176320000000000\left(-3\right)^{6}}{\left(-4\right)^{15}}\right)^{4})$$

Calculate -3 to the power of 6 and get 729.

$$sort(-27,\left(\frac{-19349176320000000000\times 729}{\left(-4\right)^{15}}\right)^{4})$$

Multiply -19349176320000000000 and 729 to get -14105549537280000000000.

$$sort(-27,\left(\frac{-14105549537280000000000}{\left(-4\right)^{15}}\right)^{4})$$

Calculate -4 to the power of 15 and get -1073741824.

$$sort(-27,\left(\frac{-14105549537280000000000}{-1073741824}\right)^{4})$$

Reduce the fraction \frac{-14105549537280000000000}{-1073741824} to lowest terms by extracting and canceling out -33554432.

$$sort(-27,\left(\frac{420378134765625}{32}\right)^{4})$$

Calculate \frac{420378134765625}{32} to the power of 4 and get \frac{31229172421194675595487288676677053445018827915191650390625}{1048576}.

$$sort(-27,\frac{31229172421194675595487288676677053445018827915191650390625}{1048576})$$

Convert decimal numbers in the list -27,\frac{31229172421194675595487288676677053445018827915191650390625}{1048576} to fractions.

$$-27,\frac{31229172421194675595487288676677053445018827915191650390625}{1048576}$$

Evaluate

$$-27,\ \frac{31229172421194675595487288676677053445018827915191650390625}{1048576}$$