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October 30th, 2014, 01:55 PM   #1
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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?
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October 30th, 2014, 05:22 PM   #2
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Quote:
Originally Posted by mathsheadache View Post
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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