Solve {l}{10^{-4}*10^{-3}*(10^{-2})^-2}{10^4*(10^-1)^4}

$$\left. \begin{array} { l } { 10 ^ { - 4 } \times 10 ^ { - 3 } \times ( 10 ^ { - 2 } ) ^ { - 2 } } \\ { 10 ^ { 4 } \times ( 10 ^ { - 1 } ) ^ { 4 } } \end{array} \right.$$

Sort

$$\frac{1}{1000},\ 1$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply -2 and -2 to get 4.

$$sort(10^{-4}\times 10^{-3}\times 10^{4},10^{4}\times \left(10^{-1}\right)^{4})$$

To multiply powers of the same base, add their exponents. Add -4 and -3 to get -7.

$$sort(10^{-7}\times 10^{4},10^{4}\times \left(10^{-1}\right)^{4})$$

To multiply powers of the same base, add their exponents. Add -7 and 4 to get -3.

$$sort(10^{-3},10^{4}\times \left(10^{-1}\right)^{4})$$

To raise a power to another power, multiply the exponents. Multiply -1 and 4 to get -4.

$$sort(10^{-3},10^{4}\times 10^{-4})$$

Multiply 10^{4} and 10^{-4} to get 1.

$$sort(10^{-3},1)$$

Calculate 10 to the power of -3 and get \frac{1}{1000}.

$$sort(\frac{1}{1000},1)$$

Convert decimal numbers in the list \frac{1}{1000},1 to fractions.

$$\frac{1}{1000},1$$

Evaluate

$$\frac{1}{1000},\ 1$$