The question is an illustration of proportion and exponents
The number of dvd is one crate is: [tex]\mathbf{5^3\ dvds}[/tex]
From the question, the given parameters are:
[tex]\mathbf{5\ dvd = 1\ wrap}[/tex] ---- 5 dvds in 1 package
[tex]\mathbf{5\ package = 1\ box}[/tex] --- 5 packages in 1 box
[tex]\mathbf{5\ boxes = 1\ crate}[/tex] --- 5 boxes in 1 crate
The number of dvds in 1 crate is calculated as follows:
[tex]\mathbf{5\ boxes = 1\ crate}[/tex]
Substitute 5 packages for 1 box in the above equation
[tex]\mathbf{5 \times 5\ packages = 1\ crate}[/tex]
Substitute 5 dvds for 1 package in the above equation
[tex]\mathbf{5 \times 5 \times 5\ dvd= 1\ crate}[/tex]
Apply law of indices
[tex]\mathbf{5^{1 + 1 + 1}\ dvd= 1\ crate}[/tex]
Express properly as:
[tex]\mathbf{5^3\ dvd= 1\ crate}[/tex]
Rewrite as:
[tex]\mathbf{1\ crate = 5^3\ dvd}[/tex]
Hence, the number of dvd is one crate is: [tex]\mathbf{5^3\ dvds}[/tex]
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