Find the value of x, if x raised to the power 5 equals to (5/7) raised to the power -3 × (-5/7) raised to the power 8

Asked by palaktapadiya08.8spicertl | 3rd Jun, 2020, 02:21: PM

Expert Answer:

We need to find the value of x if it is given that x5 = (5/7)-3 x (-5/7)8
This question can be solved using laws of exponents as follows:
x5 = (5/7)-3 x (-5/7)8
x5 = (5/7)-3 x (-1)8 x (5/7)8   ...  Using the property (ab)m = am x bm
x5 = (5/7)-3 x (5/7)8   
Using the property, am x an = am+n, we get
x5 = (5/7)-3+8
x5 = (5/7)5
Using the property that if am = bm then a = b, we get
x = 5/7
Hence, the value of x is 5/7.

Answered by Renu Varma | 3rd Jun, 2020, 04:44: PM