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Evaluate : 9^((5)/(2)) - 3xx8^(0)-((1...

Evaluate :
`9^((5)/(2)) - 3xx8^(0)-((1)/(81))^(-(1)/(2))`

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The correct Answer is:
To evaluate the expression \( 9^{\frac{5}{2}} - 3 \times 8^{0} - \left(\frac{1}{81}\right)^{-\frac{1}{2}} \), we can break it down step by step. ### Step 1: Evaluate \( 8^0 \) Any number raised to the power of 0 is equal to 1. Therefore: \[ 8^{0} = 1 \] So, the expression simplifies to: \[ 9^{\frac{5}{2}} - 3 \times 1 - \left(\frac{1}{81}\right)^{-\frac{1}{2}} \] ### Step 2: Substitute the value of \( 8^0 \) Now substituting the value we found: \[ 9^{\frac{5}{2}} - 3 - \left(\frac{1}{81}\right)^{-\frac{1}{2}} \] ### Step 3: Evaluate \( 9^{\frac{5}{2}} \) We can rewrite \( 9 \) as \( 3^2 \): \[ 9^{\frac{5}{2}} = (3^2)^{\frac{5}{2}} = 3^{2 \times \frac{5}{2}} = 3^5 \] Calculating \( 3^5 \): \[ 3^5 = 3 \times 3 \times 3 \times 3 \times 3 = 243 \] So now our expression is: \[ 243 - 3 - \left(\frac{1}{81}\right)^{-\frac{1}{2}} \] ### Step 4: Evaluate \( \left(\frac{1}{81}\right)^{-\frac{1}{2}} \) We can rewrite \( \frac{1}{81} \) as \( 81^{-1} \), so: \[ \left(\frac{1}{81}\right)^{-\frac{1}{2}} = 81^{\frac{1}{2}} = \sqrt{81} = 9 \] Now substituting this back into the expression: \[ 243 - 3 - 9 \] ### Step 5: Simplify the expression Now we can simplify: \[ 243 - 3 = 240 \] Then: \[ 240 - 9 = 231 \] ### Final Answer Thus, the value of the expression is: \[ \boxed{231} \]
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