An anthropologist finds bone that her instruments measure it as 0.717% of the amount of carbon-14 the bones would have contained when the person was alive. how long ago did the person die?
the half life of carbon 14 is 5,730 years. round your answer to the nearest thousand.

hey there!

"which expression is equivalent to ? "

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use this rule: (x^a)^b = x^ab

3(x + 2)^3/5 + 2 = 27

subtract 3 from both sides

3(x + 2)^3/5 = 27 - 3

simplify 27 - 3 to 24

3(x + 2)^3/5 = 24

divide both sides by 3

(x + 2)^3/5 = 24/3

simplify 24/3 to 8

(x + 2)^3/5 = 8

take the cube root of both sides

x + 2 = 3/5√8

invert and multiply

x + 2 = 8^5/3

calculate

x + 2 = 2^5

simplify 2^5 to 32

x + 2 = 32

subtract 2 from both sides

x = 32 - 2

simplify 32 - 3 to 30

x = 30

hello from mrbilldoesmath!

discussion:

consider this example:

3 ^ 4 = 3 * 3 * 3 *3 = 81

but it also equals

(1/3) ^ (-4)   =   1 / ( 1/3)^4 = 1 / (1/81) = 81

the exponent appears in the denominator.   is this what you meant?

you,

mrb