Question

$$\left. \begin{array} { l } { ( 1000 ) ^ { 9 } \div ( 100 ) ^ { 29 } = ? } \\ { ( 10 ^ { 3 } ) ^ { 9 } - ( 160 ) ^ { 24 } - 9 ) } \end{array} \right.$$

Answer

[No Solution]

Solution


Simplify  \({1000}^{9}\)  to  \(1.0\times {10}^{27}\).
\[\frac{1.0\times {10}^{27}}{{10}^{29}}=10124\]
Simplify  \(1.0\times {10}^{27}\)  to  \({10}^{27}\).
\[\frac{{10}^{27}}{{10}^{29}}=10124\]
Use Quotient Rule: \(\frac{{x}^{a}}{{x}^{b}}={x}^{a-b}\).
\[{10}^{27-29}=10124\]
Simplify  \(27-29\)  to  \(-2\).
\[{10}^{-2}=10124\]
Use Negative Power Rule: \({x}^{-a}=\frac{1}{{x}^{a}}\).
\[\frac{1}{{10}^{2}}=10124\]
Simplify  \({10}^{2}\)  to  \(100\).
\[\frac{1}{100}=10124\]
Since \(\frac{1}{100}=10124\) is false, there is no solution.
No Solution