Question

7^.34
how do you get the answer when you power a decimal?

Answer 1

we could change the decimal to a fraction, do you know how fractional powers?

Answer 2

how fractional powers work*

Answer 3

34/100

Answer 4

yep, and simplified:

17/50

Answer 5

then whats the next step?

Answer 6

so:

\[7^{0.34} = 7^{\frac{17}{50}} = (7^{17})^{\frac{1}{50}}=\sqrt[50]{7^{17}}\]

Answer 7

well you see i knew how to do that ... but i don't know how to apply this to my problem which is
f(x) = 15,000x^.34
f(7)

Answer 8

can you use a calculator?

Answer 9

yes

Answer 10

what happens if you just try to type in 15000*(7^(0.34)) ?

Answer 11

well its easy on the calculator but i want to learn how to do it not just depend on a calculator... do you know how to solve it? manually?

Answer 12

yes, like above first we know 7^(0.34) = 7^(17/50)

so we calculate 7^15 , which comes to a very big number
about 4.74756151 × 10^12
then we take the 50th root of that number

which would take us ages, and is really why we use a calculator

alternatively if you have log tables and know how to use them then that would help you get a quick estimate

Answer 13

thank you so much

Answer 14

happy to help :)