Question

If \(\left(\frac{5}{3}\right)^{-5}\times \left(\frac{5}{3}\right)^{-11}=\left(\frac{5}{3}\right)^{8x}\) find the value of 'x'
1. 2
2. -1
3. 1
4. -2

Answer 1

Correct Answer - Option 4 : -2

Formula used:

a^m × aⁿ = a^{m + n}

a^m = aⁿ (Where, base is same)

m = n

Calculation:

\(\left(\frac{5}{3}\right)^{-5}× \left(\frac{5}{3}\right)^{-11}=\left(\frac{5}{3}\right)^{8x}\)

⇒ \(\left(\frac{5}{3}\right)^{-5 -11} =\left(\frac{5}{3}\right)^{8x}\)

⇒ \(\left(\frac{5}{3}\right)^{-16} =\left(\frac{5}{3}\right)^{8x}\)

⇒ -16 = 8x

⇒ x = -2

∴ The value of x is -2.