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Evaluate the expression. Do not round your answer.

(1)/(3)(4*3)+2^(3)=

Evaluate the expression. Do not round your answer.\newline13(43)+23= \frac{1}{3}(4 \cdot 3)+2^{3}=

Full solution

Q. Evaluate the expression. Do not round your answer.\newline13(43)+23= \frac{1}{3}(4 \cdot 3)+2^{3}=
  1. Identify Components: Identify the components of the expression.\newlineThe expression is (13)(4×3)+23(\frac{1}{3})(4\times3)+2^{3}. It consists of a fraction (13)(4×3)(\frac{1}{3})(4\times3) and an addition of 232^{3}.
  2. Simplify Fraction: Simplify the fraction part of the expression.\newlineThe fraction part is (1)/(3)(43)(1)/(3)(4*3). First, multiply the numbers in the denominator: 43=124*3 = 12. Then, the fraction becomes (1)/(312)(1)/(3*12).
  3. Continue Simplifying: Continue simplifying the fraction.\newlineNow, multiply 3×123\times12 to get 3636. So, the fraction is (1)/(36)(1)/(36).
  4. Simplify Exponentiation: Simplify the exponentiation part of the expression.\newlineThe exponentiation part is 232^{3}. Calculate 23=2×2×2=82^3 = 2\times2\times2 = 8.
  5. Add Results: Add the results of the fraction and the exponentiation.\newlineNow, add the simplified fraction 136\frac{1}{36} to the result of 232^3, which is 88. So, the expression becomes 136+8\frac{1}{36} + 8.
  6. Convert to Fraction: Convert the whole number to a fraction with the same denominator to add them.\newlineTo add 88 to 136\frac{1}{36}, convert 88 to a fraction with the denominator 3636: 8=8×3636=288368 = 8\times\frac{36}{36} = \frac{288}{36}.
  7. Add Fractions: Add the two fractions.\newlineNow, add 136\frac{1}{36} to 28836\frac{288}{36} to get (1+28836)=28936\left(\frac{1 + 288}{36}\right) = \frac{289}{36}.

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