Find the value of p so that (3/5) raised to the power 3 ÷ (3/5) raised to the power -3 = (3/5) raised to the power 3p

Asked by palaktapadiya08.8spicertl | 3rd Jun, 2020, 02:23: PM

Expert Answer:

It is given that: (3/5)3 ÷ (3/5)-3 = (3/5)3p and we need to find the value of p.
This question can be solved using laws of exponents as follows:
(3/5)3/(3/5)-3 = (3/5)3p
Using the law of exponent 1/am = a-m, we have
(3/5)3 x (3/5)-(-3) = (3/5)3p
(3/5)3 x (3/5)3 = (3/5)3p
Using the law of exponent am x an = am+n, we get
(3/5)3+3 = (3/5)3p
(3/5)6 = (3/5)3p
Using the property of exponent that if am = an then m = n, we have
6 = 3p
p = 6/3
p = 2

Answered by Renu Varma | 3rd Jun, 2020, 04:33: PM