# Simplify (-a^(2b^-2))÷((a^(-2b^8))/(a^(4b^-2)))

-a2b-2÷a-2b8a4b-2
To divide by a fraction, multiply by its reciprocal.
-a2b-2a4b-2a-2b8
Rewrite the expression using the negative exponent rule b-n=1bn.
-a21b2a4b-2a-2b8
Combine 2 and 1b2.
-a2b2a4b-2a-2b8
Cancel the common factor of a4b-2 and a-2b8.
Factor a-2b8 out of a4b-2.
-a2b2a-2b8a4b-2+2b8a-2b8
Cancel the common factors.
Multiply by 1.
-a2b2a-2b8a4b-2+2b8a-2b8⋅1
Cancel the common factor.
-a2b2a-2b8a4b-2+2b8a-2b8⋅1
Rewrite the expression.
-a2b2a4b-2+2b81
Divide a4b-2+2b8 by 1.
-a2b2a4b-2+2b8
-a2b2a4b-2+2b8
-a2b2a4b-2+2b8
Multiply a2b2 by a4b-2+2b8 by adding the exponents.
Move a4b-2+2b8.
-(a4b-2+2b8a2b2)
Use the power rule aman=am+n to combine exponents.
-a4b-2+2b8+2b2
Simplify each term.
Rewrite the expression using the negative exponent rule b-n=1bn.
-a41b2+2b8+2b2
Combine 4 and 1b2.
-a4b2+2b8+2b2
-a4b2+2b8+2b2
Combine fractions with similar denominators.
-a2b8+4+2b2
-a2b8+6b2
-a2b8+6b2
To write 2b8 as a fraction with a common denominator, multiply by b2b2.
-a2b8b2b2+6b2
Combine the numerators over the common denominator.
-a2b8b2+6b2
Simplify the numerator.
Factor 2 out of 2b8b2+6.
Factor 2 out of 2b8b2.
-a2(b8b2)+6b2
Factor 2 out of 6.
-a2(b8b2)+2⋅3b2
Factor 2 out of 2(b8b2)+2⋅3.
-a2(b8b2+3)b2
-a2(b8b2+3)b2
Multiply b8 by b2 by adding the exponents.
Use the power rule aman=am+n to combine exponents.
-a2(b8+2+3)b2