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.

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!

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!

Join our real-time social learning platform and learn together with your friends!