John Estrada
01/22/2024 · Junior High School
\( \left[\begin{array}{c}{\left[\begin{array}{c}{(8^{2}\times 4^{3})\div (2^{3})^{3}}\end{array}\right]\div (32^{2}\div 8^{3})}\end{array}\right]\div (8^{4}\div 4^{3}\div 2^{5}) \)
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Step-by-step Solution
Calculate or simplify the expression \( \left[\left[(8^{2}\times 4^{3})\div (2^{3})^{3}\right]\div (32^{2}\div 8^{3})\right]\div (8^{4}\div 4^{3}\div 2^{5}) \).
Calculate the value by following steps:
- step0: Calculate:
\(\left(\left(\left(8^{2}\times 4^{3}\right)\div \left(2^{3}\right)^{3}\right)\div \left(32^{2}\div 8^{3}\right)\right)\div \left(8^{4}\div 4^{3}\div 2^{5}\right)\)
- step1: Multiply the exponents:
\(\left(\left(\left(8^{2}\times 4^{3}\right)\div 2^{3\times 3}\right)\div \left(32^{2}\div 8^{3}\right)\right)\div \left(8^{4}\div 4^{3}\div 2^{5}\right)\)
- step2: Multiply the numbers:
\(\left(\left(2^{12}\div 2^{3\times 3}\right)\div \left(32^{2}\div 8^{3}\right)\right)\div \left(8^{4}\div 4^{3}\div 2^{5}\right)\)
- step3: Multiply the numbers:
\(\left(\left(2^{12}\div 2^{9}\right)\div \left(32^{2}\div 8^{3}\right)\right)\div \left(8^{4}\div 4^{3}\div 2^{5}\right)\)
- step4: Divide the terms:
\(\left(2^{3}\div \left(32^{2}\div 8^{3}\right)\right)\div \left(8^{4}\div 4^{3}\div 2^{5}\right)\)
- step5: Divide the terms:
\(\left(2^{3}\div 2\right)\div \left(8^{4}\div 4^{3}\div 2^{5}\right)\)
- step6: Divide the terms:
\(2^{2}\div \left(8^{4}\div 4^{3}\div 2^{5}\right)\)
- step7: Divide the terms:
\(2^{2}\div \left(2^{6}\div 2^{5}\right)\)
- step8: Divide the terms:
\(2^{2}\div 2\)
- step9: Rewrite the expression:
\(\frac{2^{2}}{2}\)
- step10: Divide the numbers:
\(2^{2-1}\)
- step11: Calculate:
\(2\)
The result of the expression \( \left[\left[(8^{2}\times 4^{3})\div (2^{3})^{3}\right]\div (32^{2}\div 8^{3})\right]\div (8^{4}\div 4^{3}\div 2^{5}) \) is 2.
Quick Answer
El resultado de la expresión es 2.
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