Author Topic: exponential help (Read 537 times) Tweet Share

Sanguinne · « **on:** March 16, 2013, 01:42:13 pm »

does anyone know how to solve these two problems?

1)simplify (x^2+y^2)/(x^(-2) + y^(-2)

and

2) solve for n (27 x 3^n)^n=27^n + 3^(1/4)

Conic · « **Reply #1 on:** March 16, 2013, 02:46:21 pm »

1. Use $x^{-2}=\frac{1}{x^2}$ :

Spoiler

$\frac{x^2+y^2}{x^{-2}+y^{-2}}$

$=\frac{x^2+y^2}{\frac{1}{x^2}+\frac{1}{y^2}}$

$=\frac{x^2+y^2}{\frac{x^2+y^2}{x^2y^2}}$

$=x^2y^2$

2. Note that $3^3=27$ , and that $x^n*x^m=x^{m+n}$ :

Spoiler

$(27*3^n)^n=27^n*3^\frac{1}{4}$

$(3^3*3^n)^n=3^{3n}*3^\frac{1}{4}$

$(3^{n+3})^n=3^{3n+\frac{1}{4}}$

$3^{n^2+3n}=3^{3n+\frac{1}{4}}$

$n^2+3n=3n+\frac{1}{4}$

$n^2=\frac{1}{4}$

$n=\pm\frac{1}{2}$

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Author Topic: exponential help (Read 537 times) Tweet Share

Sanguinne

exponential help

Conic

Re: exponential help

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