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Evaluate the expression (1)/(4)(2)^(x) for x=5.

Evaluate the expression 14(2)x \frac{1}{4}(2)^{x} for x=5 x=5 .

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Full solution

Q. Evaluate the expression 14(2)x \frac{1}{4}(2)^{x} for x=5 x=5 .
  1. Substitute xx with 55: We are given the expression 142x\frac{1}{4}2^{x} and the value of xx as 55. We need to substitute xx with 55 in the expression.\newlineSubstitute 55 for xx in the expression 142x\frac{1}{4}2^{x}.\newline5500
  2. Calculate 22 raised to the power of 55: Calculate the value of 22 raised to the power of 55.\newline25=2×2×2×2×22^{5} = 2 \times 2 \times 2 \times 2 \times 2\newline=32= 32
  3. Plug the value of 252^5 into the expression: Now, plug the value of 252^{5} into the original expression.\newline14(2)5\frac{1}{4}(2)^{5} becomes 14×32\frac{1}{4 \times 32}
  4. Multiply 44 by 3232: Multiply 44 by 3232 to find the denominator.\newline4×32=1284 \times 32 = 128
  5. Write the expression with the calculated denominator: Write the expression with the calculated denominator. (1)/(4×32)(1)/(4 \times 32) becomes (1)/(128)(1)/(128)
  6. Simplify the expression: Simplify the expression to find the final value. (1)/(128)=0.0078125(1)/(128) = 0.0078125

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