Work out the value of 81^(-1/4) (Non-Calculator)

To answer this question, we have to think about our power rules and use them to slowly simplify this complicated expression:81^-1/4 = ((81)^1/2)^-1/2 (Because ((x)^y)^z = x^yz - one of our 3 power rules)We know that 9² = 81 so if we do a power of 1/2 on both sides we get:9 = 81^1/2So: 81^-1/4 = 9^-1/2We can use a similar line of reasoning to get down to:81^-1/4= 3^-1We also know that a number raised to the power of -1 is equal to 1 divided by that number (x^-1 = 1/x)So:81^-1/4 = 1/3