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# simplify: 34f6g4h5 over 8f8g3h7

Hello Matilda,

This question is of simplifying exponents. In this division sum we first reduce the coefficient and then we will take care of bases and exponents. If you look at the problem there are three bases f, g and h and since it is division problem we'll use the division exponent formula. Remember when we do division in exponents we subtract the powers. We'll use this (xm / xn = xm-n). You can use the formula other way also (xm / xn = 1/xn-m). Look in this formula we have same base x and powers are m and n.

There are two ways:

1. Since the powers are small we can expand and do it. But with higher powers we can't use this method

34 f6 g4 h5 / 8 f8 g3 h7 = 2. 17. f.f.f.f.f.f.g.g.g.g.h.h.h.h.h / 2.2.2.f.f.f.f.f.f.f.f.g.g.g.h.h.h.h.h.h.h

Using reducing fraction concept we'll cancel common factors from numerator and denominator. We'll get

17.g / 2.2.f.f.h.h = 17g/4f2h2 (answer)

2. The above method will not work for higher powers. I did just to make you understand how it works. Now we'll use the formula

34 f6 g4 h5 / 8 f8 g3 h= 2.17.g4-3 / 2.2.2.f8-6.h7-5 = 17.g1 / 2.2. f2. h2 = 17g / 4f2h2(answer)

Hope this helps.

(34f6g4h5) /(8f8g3h7)

= (34/8)(f6/f8)(g4/g3)(h5/h7), you group like factors here

= (17/4)(1/f2)(g)(1/h2), make sure there is no "-" exponent in your final answer.

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