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If $w = 2^{230} × 3^{234} × 5^{236}$, $x = 2^{232} × 3^{233} × 5^{235}$,$y = 2^{230} × 3^{233} × 5^{235}$ and $z = 2^{231} × 3^{234} × 5^{235}$ then the order from smallest to largest is:

At first, I thought that the one of the largest exponent on the bigger number would be greater, however that turned out to be incorrect. may you please give me an accurate way to do this question

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    Hint: You can ignore the common factor $2^{230} \cdot 3^{233} \cdot 5^{235}$ – 2017-01-25

2 Answers 2

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Hint:

Take $2^{230}\times3^{233}\times5^{235}$ common from $w,x,y,z$, and then compare.

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Assuming $a = 2^{230} \times 3^{233} \times 5^{235}$

Then: $w = a \cdot 3 \cdot 5$, $x = a \cdot 2 \cdot 2$, $y = a$ and $z = a \cdot 2 \cdot 3$

Therefore: $y < x < z < w$.