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The value of (64)-2/3 x (27) -2/3 is
- a)1/144
- b)1/145
- c)1/414
- d)1/444
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
The value of (64)-2/3x (27)-2/3 isa)1/144b)1/145c)1/414d)1/444Correct ...
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The value of (64)-2/3x (27)-2/3 isa)1/144b)1/145c)1/414d)1/444Correct ...
Expression Simplification:
- First, simplify each term inside the parentheses:
- (64)^(-2/3) = 1/(64)^(2/3) = 1/(4^2) = 1/16
- (27)^(-2/3) = 1/(27)^(2/3) = 1/(3^3) = 1/27
- Substitute the simplified values back into the expression:
- 1/16 - 2/3 * 1/27
- 1/16 - 2/81
- To combine the fractions, find a common denominator, which is 16*81 = 1296:
- (1*81)/(16*81) - (2*16)/(81*16)
- 81/1296 - 32/1296
- (81 - 32)/1296
- 49/1296
Final Answer:
- The final simplified value of the expression (64)^(-2/3) - 2/3 * (27)^(-2/3) is 49/1296, which can be further simplified to 1/144. Therefore, the correct answer is option 'A' - 1/144.
- First, simplify each term inside the parentheses:
- (64)^(-2/3) = 1/(64)^(2/3) = 1/(4^2) = 1/16
- (27)^(-2/3) = 1/(27)^(2/3) = 1/(3^3) = 1/27
- Substitute the simplified values back into the expression:
- 1/16 - 2/3 * 1/27
- 1/16 - 2/81
- To combine the fractions, find a common denominator, which is 16*81 = 1296:
- (1*81)/(16*81) - (2*16)/(81*16)
- 81/1296 - 32/1296
- (81 - 32)/1296
- 49/1296
Final Answer:
- The final simplified value of the expression (64)^(-2/3) - 2/3 * (27)^(-2/3) is 49/1296, which can be further simplified to 1/144. Therefore, the correct answer is option 'A' - 1/144.
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