## anonymous 5 years ago how can I simpify the following (preferably, without using a calculator): a) (3^3)/(squareRoot(3^5)) b) 4ln(squareRoot(x))+6ln(x^(1/3)) p.s. i use squareRoot() beacause i dont know how to write a root symbol.

1. anonymous

Is this the correct form? a) $3^3 / \sqrt{3^5}$ b) $4 \ln \sqrt{x} + 6lnx^{1/3}$ I won't be able to get back to you for a while, so sorry if I can't continue to help. But my advice for a) is to first convert the denominator into a form in which simplifying is simple. For b) remember your logarithmic identities, and combine the terms into a simplified logarithm; once again, remember your special rules with exponents (and logarithms!). Good luck!

2. anonymous

Here are the rules: For a) $x^{a}x ^{b}=x ^{a+b}$ *remember you can rewrite a root as a fractional exponent, and a denominator as a negative exponent, for example: $\sqrt{x}=x ^{1/2}$ $1/\sqrt{x}=x ^{-1/2}$ For b) $a \ln (x)=\ln (x ^{a})$ and $\ln (a)+\ln (b)=\ln (ab)$ Hope that helps!