Washington Henry
01/12/2023 · Primary School
8) \( \frac{5^{-3}}{3^{7}}:\left(\frac{5^{2}}{3^{-3}}\right)^{-2} \)
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Tutor-Verified Answer
Step-by-step Solution
Calculate or simplify the expression \( (5^(-3)/3^7)/((5^2/3^(-3))^(-2)) \).
Calculate the value by following steps:
- step0: Calculate:
\(\frac{\left(\frac{5^{-3}}{3^{7}}\right)}{\left(\left(\frac{5^{2}}{3^{-3}}\right)^{-2}\right)}\)
- step1: Evaluate:
\(\frac{\left(\frac{5^{-3}}{3^{7}}\right)}{\left(\frac{5^{2}}{3^{-3}}\right)^{-2}}\)
- step2: Remove the parentheses:
\(\frac{\frac{5^{-3}}{3^{7}}}{\left(\frac{5^{2}}{3^{-3}}\right)^{-2}}\)
- step3: Divide the terms:
\(\frac{\frac{5^{-3}}{3^{7}}}{675^{-2}}\)
- step4: Divide the terms:
\(\frac{\frac{1}{273375}}{675^{-2}}\)
- step5: Express with a positive exponent:
\(\frac{\frac{1}{273375}}{\frac{1}{675^{2}}}\)
- step6: Multiply by the reciprocal:
\(\frac{1}{273375}\times 675^{2}\)
- step7: Rewrite the expression:
\(\frac{1}{675\times 405}\times 675^{2}\)
- step8: Reduce the numbers:
\(\frac{1}{3}\times 5\)
- step9: Multiply:
\(\frac{5}{3}\)
The simplified form of the expression \( \frac{5^{-3}}{3^{7}}:\left(\frac{5^{2}}{3^{-3}}\right)^{-2} \) is \( \frac{5}{3} \) or \( 1\frac{2}{3} \) or \( 1.\dot{6} \).
Quick Answer
The simplified form is \( \frac{5}{3} \) or \( 1\frac{2}{3} \) or \( 1.\dot{6} \).
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