How do you simplify #(5^sqrt2)^sqrt8#? Precalculus Exponential and Logistic Modeling Exponential Growth and Decay 1 Answer Alan P. Oct 29, 2016 #(5^sqrt(2))^sqrt(8) = color(green)(625)# Explanation: For the general case #color(white)("XXX")(x^a)^b= x^(ab)# So #color(white)("XXX")(5^sqrt(2))^sqrt(8) = 5^sqrt(16)=5^4=625# Answer link Related questions How do I find an exponential growth function in terms of #t#? What is exponential growth? How do I find the multiplier for a rate of exponential decay? How is exponential decay related to a half-life? How to find an equation of exponential decay? What happens when something grows exponentially? How long does it take the culture to double its mass if a bacterial culture which is growing... Joe Smith invest his inheritance of $50,000 in an account paying 6.5% interest. If interest is... How do you write an exponential equation that passes through (1, 1.5), (-1, 6)? How do you write an exponential equation that passes through (0,3) and (2,6)? See all questions in Exponential Growth and Decay Impact of this question 1439 views around the world You can reuse this answer Creative Commons License