Work out 5r4/55r4

Mathematics

ScanSolve AI Answer

Answer

1625\frac{1}{625}

Step-by-step solution

6 steps

Let's simplify the expression.

  1. Separate the terms with the same base.

    5r455r4=5155×r4r4\frac{5r^4}{5^5r^4} = \frac{5^1}{5^5} \times \frac{r^4}{r^4}

  2. Apply the rule of exponents for division, aman=am−n\frac{a^m}{a^n} = a^{m-n}, to both parts.

    For the base 5 terms:

    5155=51−5=5−4\frac{5^1}{5^5} = 5^{1-5} = 5^{-4}

    For the base r terms:

    r4r4=r4−4=r0\frac{r^4}{r^4} = r^{4-4} = r^0

  3. Simplify the terms.

    Remember that any non-zero number raised to the power of 0 is 1 (r0=1r^0 = 1). Also, a−n=1ana^{-n} = \frac{1}{a^n}.

    5−4=1545^{-4} = \frac{1}{5^4} r0=1r^0 = 1

  4. Multiply the simplified terms.

    154×1=154\frac{1}{5^4} \times 1 = \frac{1}{5^4}

  5. Calculate the value of 545^4.

    54=5×5×5×5=25×25=6255^4 = 5 \times 5 \times 5 \times 5 = 25 \times 25 = 625

  6. Write the final simplified expression.

    1625\frac{1}{625}
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