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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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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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ICSE-INDICES [EXPONENTS]-EXERCISE 7 (C)
  1. Evaluate : 9^((5)/(2)) - 3xx8^(0)-((1)/(81))^(-(1)/(2))

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  2. Evaluate : (64)^((2)/(3))-root(3)(125)-(1)/(2^(-5))+(27)^(-(2)/(3))...

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  3. Evaluate : [(-(2)/(3))^(-2)]^(3)xx((1)/(3))^(-4)xx3^(-1)xx(1)/(6)

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  4. Simplify : (3xx9^(n+1)-9xx3^(2n))/(3xx3^(2n+3)-9^(n+1))

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  5. Solve : 3^(x-1)xx5^(2y-3)=225.

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  6. If ((a^(-1)b^(2))/(a^(2)b^(-4)))div((a^(3)b^(-5))/(a^(-2)b^(3)))=a^(x)...

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  7. If 3^(x +1) = 9^(x - 3), find the value of 2^(1 + x).

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  8. If 2^(x)=4^(y)=8^(z) and (1)/(2x)+(1)/(4y)+(1)/(8z)=4 find the value o...

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  9. If (9^n\ x\ 3^2\ x\ 3^n-\ 27^n)/(3^(3m)\ x\ 2^3)=1/(27) , prove that m...

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  10. Solve for x : x:(13)^sqrt(x)=4^(4)-3^(4)-6.

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  11. If 3^(4x)=(81)^(-1)and(10)^((1)/(y))=0.0001, value of 2^(-x) xx 16^(y)...

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  12. Solve the equation: 3(2^x+1)-2^(x+2)+5=0

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  13. If (a^(m))^(n)=a^(m).a^(n), find the value of : m(n - 1) - (n - 1)

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  14. If m = root(3)(15) and n = root(3)(14), find the value of m - n - (1)/...

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  15. Evaluate : (2^(n)xx6^(m+1)xx10^(m-n)xx15^(m+n-2))/(4^(m)xx3^(2m+n)xx25...

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  16. Evaluate : ((x^(q))/(x^(r )))^((1)/(qr))xx((x^(r ))/(x^(p)))^((1)/(rp)...

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  17. Prove that: (a^(-1))/(a^(-1)+b^(-1))+(a^(-1))/(a^(-1)-b^(-1))=(2b^2)/(...

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  18. Prove that: (a+b+c)/(a^(-1)\ b^(-1)+b^(-1)\ c^(-1)+c^(-1)a^(-1))=a b c

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  19. Evaluate : (4)/((216)^(-2//3))+(1)/((256)^(-3//4))+(2)/((343)^(-1//3)...

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