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 October 30th, 2014, 01:55 PM #1 Newbie   Joined: Oct 2014 From: London Posts: 27 Thanks: 0 Help with these surd equations?! I have these equations 1.$\displaystyle \frac{5^2x5^{-3}}{5^{-4}x5^{6}}$ 2.$\displaystyle \frac{(x^5y^3)^4}{x^3y^2}$ 3.$\displaystyle \frac{\sqrt{6}+4}{\sqrt{4}}$ Any help?
October 30th, 2014, 05:22 PM   #2
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 Originally Posted by mathsheadache I have these equations 1.$\displaystyle \frac{5^2x5^{-3}}{5^{-4}x5^{6}}$ 2.$\displaystyle \frac{(x^5y^3)^4}{x^3y^2}$ 3.$\displaystyle \frac{\sqrt{6}+4}{\sqrt{4}}$ Any help?
1.$\displaystyle \frac{5^2x5^{-3}}{5^{-4}x5^{6}}$

the x factors in the numerator & denominator divide out to 1

numerator ... $\displaystyle 5^2 \cdot 5^{-3} = 5^{-1}$

denominator ... $\displaystyle 5^{-4} \cdot 5^6 = 5^2$

$\displaystyle \frac{5^{-1}}{5^2} = 5^{-1-2} = 5^{-3} = \frac{1}{5^3}$

2. $\displaystyle \frac{(x^5y^3)^4}{x^3y^2}$

$\displaystyle \frac{x^{20}y^{12}}{x^3y^2}$ ... now use the rule for division for exponents

3. $\displaystyle \frac{\sqrt{6}+4}{\sqrt{4}}$

come on ... what is $\displaystyle \sqrt{4}$ ?

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