Question

Simplify the expression . Assume x>0 .A) The answer can be written in the form xa wherethe exponent a is: Note: enter the exponent as a reduced fraction or integer.B) The answer can be written in the form 1xb wherethe exponent b is: Note: enter the exponent as a reduced fraction or integer.

Answer 1

the exponent a is -21/20

the exponent b is 21/20

Step-by-step explanation:

When we have a division of two power with the same base, we can subtract the exponents. So, the expression is equivalent to

`\frac{x^{-(4)/(5)}}{x^{(1)/(4)}}=x^{-(4)/(5)-(1)/(4)}=x^{-(21)/(20)}`

Additionally, when the exponent is negative, we can write the expression with a positive exponent as follows

`x^{-(21)/(20)}=\frac{1}{x^{(21)/(20)}}`

Therefore, the answers are:

the exponent a is -21/20

the exponent b is 21/20