Algebra 2 equivalent expression

Question

Which expression is equivalent to ( (1/x)^-2/3)⁶ ?

(a) 1/x⁴

(b) 1/⁴√x

(c) x⁴

(d) x

Answer 1

One rule for exponents says that if something raised to a power is raised to a power, then we multiply powers.

{Read that again slower.}

Another rule for exponents says that if we have a negative exponent, the base cuts a flip and breaks off the negative sign, so we'd have its reciprocal.

{You'll always break something doing flips in the house.}

The one you see first is the one you apply first.

Either way you get x⁴.