Answer:
a.
b.
Explanation:
a.
Original equation:
So (-x)^4 can be seen as (-x * -x) * (-x * -x), which becomes x^2 * x^2 = x^4, the negatives cancel out of the degree is even. So it becomes:
Cancel out one of the x's on the left fraction:
Rewrite the exponent in the numerator:
Simplify the numerator:
Keep numerator, change division to multiplication, flip the denominator:
multiply the denominator using the exponent identity:
Multiply the numerators and denominators:
Use the fact that:
to divide the x^3 and x^(5/3) and divide the 4 by the -8
Rewrite the exponent using the exponent identity:
Rewrite as two radicals:
Simplify:
b.
Rewrite the 4 as 2^2
Use the exponent identity:
Use the exponent identity:
Rewrite this part using the definition of a negative exponent:
.
Multiply:
rewrite 64 as 2^6
Use the identity:
Use the identity:
rewrite using the definition of a negative exponent: