On Monday, Dia ran 1 1/5 hours and traveled 6 miles. What was her average speed that day?
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Hello!
The first thing you should notice is that the exponent will be less than 1, as raising 27 to any power greater than 1 will make it larger, and you're trying to figure out what makes it equal to 3, a number less than 27.
Raising a number to a fractional power is taking its nth root:
is ![\sqrt[3]{21}](https://tex.z-dn.net/?f=%20%5Csqrt%5B3%5D%7B21%7D%20)
, so you'll really need to take the nth root of 27 to get 3. To figure out which root, write the number in exponential form with a base of 3:
= 3
= 
Now, the bases are the same (they are both 3), so you can set the exponents equal to each other:
3x = 1
Divide both sides by 3 and you've isolated x:
Answer:
The first thing you should notice is that the exponent will be less than 1, as raising 27 to any power greater than 1 will make it larger, and you're trying to figure out what makes it equal to 3, a number less than 27.
Raising a number to a fractional power is taking its nth root:
Now, the bases are the same (they are both 3), so you can set the exponents equal to each other:
3x = 1
Divide both sides by 3 and you've isolated x:
Answer: