Solve, Express using positive exponents: Negative intergers as exponents, simplify if possible

Question

5a^-7 b^4

Answer 1

5a^-7*b⁴

 

Now a^-b = 1/a^b, so 5a^-7 = 5/a⁷.  Note that the 5 is not raised to the -7 power (if it were, it would be (5a)^-7), so it stays in the numerator.  Hence:

 

5a^-7*b⁴ = 5b⁴/a⁷

Answer 2

When you have a negative exponent, the base is on the wrong side of the fraction. So here, 5a^-7 should then be 5/a⁷. Therefore, 5a^-7b⁴ = (5/a⁷)b⁴.