Simplify a term

Question

Simplify (27x⁶)^1÷3.

I thought you would just multiply the exponents which would give you 27x² but apparently the answer is 3x²? Any help would be greatly appreciated :).

Answer 1

exponents multiply to get 6 x 1/3 = 2

the 2 exponent applies only to the x, 1/3 applies to 27 27^1/3 = cube root of 27 = 3

correct answer is 3x^2

to get 27x^2 the problem would have been 27(x^6)^1/3

another scenario would be if the problem had been [(27x)^6]^1/3

then the solution would have been 27^2x^2 = 729x^2

PEMDAS is the order of operations. You do operations inside parentheses (P)first, then exponents (E), then multiplication (M).

the 27x^6 means 27(x^6) with 6 only applying to the x, not to 26. exponents are done before multiplication