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A landscaper is cutting a $\newline$ $24\frac{1}{8}$ -foot rope into pieces to make fences. $\newline$ The length of each piece is $\newline$ $3\frac{1}{5}$ feet.

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Power rule with rational exponents

Full solution

Q. A landscaper is cutting a

\newline

24\frac{1}{8}

-foot rope into pieces to make fences.

\newline

The length of each piece is

\newline

3\frac{1}{5}

feet.

Convert to Improper Fractions: Convert mixed numbers to improper fractions for easier calculations. $\newline$ $24\frac{1}{8} = (24\times 8 + 1)/8 = \frac{193}{8}$ feet. $\newline$ $3\frac{1}{5} = (3\times 5 + 1)/5 = \frac{16}{5}$ feet.
Find Number of Pieces: Divide the total length of the rope by the length of each piece to find the number of pieces. $\newline$ $(193/8) \div (16/5) = (193/8) \times (5/16) = 193\times5 / 8\times16 = 965/128$ .
Simplify Fraction: Simplify the fraction to find the whole number of pieces that can be cut. $965 \div 128 = 7$ remainder $73$ , so $7$ full pieces can be cut.

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