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Rewrite the term 2ⁿ+3 using the exponent rule a^m+n = a^m x aⁿ.

Mathematics

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Answer

3

Step-by-step solution

7 steps

  1. Rewrite the term 2n+32^{n+3} using the exponent rule am+n=am×ana^{m+n} = a^m \times a^n.

    2n+3=2n×232^{n+3} = 2^n \times 2^3

  2. Substitute this back into the numerator of the expression.

    2n×23+2n3×2n\frac{2^n \times 2^3 + 2^n}{3 \times 2^n}

  3. Factor out 2n2^n from the terms in the numerator.

    2n(23+1)3×2n\frac{2^n (2^3 + 1)}{3 \times 2^n}

  4. Cancel out the common factor 2n2^n from the numerator and the denominator.

    23+13\frac{2^3 + 1}{3}

  5. Calculate the value of 232^3.

    23=2×2×2=82^3 = 2 \times 2 \times 2 = 8

  6. Substitute the value of 232^3 into the expression and simplify.

    8+13=93\frac{8 + 1}{3} = \frac{9}{3}

  7. Perform the division.

    93=3\frac{9}{3} = 3

    The simplified answer as a simple fraction is 31\frac{3}{1} or just 3.

    33
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