Question:
\[
64^{\frac13}
-
81^{\frac14}
+
625^{\frac14}
=
?
\]
\[
64^{\frac13}
-
81^{\frac14}
+
625^{\frac14}
=
?
\]
Show Hint
Memorize common perfect powers such as \(64=4^3\), \(81=3^4\), and \(625=5^4\). They appear frequently in competitive examinations.
Updated On: Jun 12, 2026
- \(8\)
- \(6\)
- \(4\)
- \(0\)
Show Solution
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The Correct Option is B
Solution and Explanation
Concept:
A fractional exponent represents a root:
\[
a^{1/n}=\sqrt[n]{a}
\]
Step 1: Evaluate \(64^{1/3}\). \[ 64^{1/3} = \sqrt[3]{64} = 4 \]
Step 2: Evaluate \(81^{1/4}\). \[ 81^{1/4} = \sqrt[4]{81} = 3 \] since \[ 3^4=81 \]
Step 3: Evaluate \(625^{1/4}\). \[ 625^{1/4} = \sqrt[4]{625} = 5 \] since \[ 5^4=625 \]
Step 4: Substitute the values. \[ 4-3+5 \] \[ =6 \] Therefore, \[ \boxed{6} \]
Step 1: Evaluate \(64^{1/3}\). \[ 64^{1/3} = \sqrt[3]{64} = 4 \]
Step 2: Evaluate \(81^{1/4}\). \[ 81^{1/4} = \sqrt[4]{81} = 3 \] since \[ 3^4=81 \]
Step 3: Evaluate \(625^{1/4}\). \[ 625^{1/4} = \sqrt[4]{625} = 5 \] since \[ 5^4=625 \]
Step 4: Substitute the values. \[ 4-3+5 \] \[ =6 \] Therefore, \[ \boxed{6} \]
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