Question

Find x so that ( 5/3)^ -5 *(5/3)^ -11 =(5/3)^ 8x​

Answer 1

Answer:

The value of x is - 2.

______________________

Given:

$\sf \bigg( \dfrac{5}{3} \bigg)^{-5} \times \bigg( \dfrac{5}{3} \bigg)^{-11} = \bigg( \dfrac{5}{3} \bigg)^{8x}$

To Find:

• Value of x.

Solution:

$\sf \bigg( \dfrac{5}{3} \bigg)^{-5} \times  \bigg( \dfrac{5}{3} \bigg)^{-11} =  \bigg( \dfrac{5}{3} \bigg)^{8x}$

Using the law of exponents,

$\sf \implies a^m \times a^n = a^{m+n}$

$\sf \implies \bigg( \dfrac{5}{3} \bigg)^{(-5)+(-11)} = \bigg( \dfrac{5}{3} \bigg)^{8x}$

Adding the exponents,

$\sf \implies \bigg( \dfrac{5}{3} \bigg)^{-16} = \bigg( \dfrac{5}{3} \bigg)^{8x}$

Let's take the exponents,

$\sf \implies -16 = 8x$

Solving the equation,

$\sf \implies \dfrac{-16}{8} = x$

$\sf \implies -2 = x$

Verification:

To verify, let's substitute the value of x.

$\sf \bigg( \dfrac{5}{3} \bigg)^{-5} \times  \bigg( \dfrac{5}{3} \bigg)^{-11} =  \bigg( \dfrac{5}{3} \bigg)^{8x}$

Substitute the value of x,

$\sf \implies \bigg( \dfrac{5}{3} \bigg)^{-5} \times  \bigg( \dfrac{5}{3} \bigg)^{-11} =  \bigg( \dfrac{5}{3} \bigg)^{8\times (-2)}$

$\sf \implies (-5) + (-11) = 8 \times (-2)$

Solving the equation,

$\sf \implies -5-11 = 8 \times -2$

$\sf \implies -16 = 8 \times -2$

$\sf \implies -16 = -16$

∵ LHS = RHS

∴ Thus, verified.

Answer 2

Answer:

Answer:

The value of x is - 2.

______________________

Given:

$\sf \bigg( \dfrac{5}{3} \bigg)^{-5} \times \bigg( \dfrac{5}{3} \bigg)^{-11} = \bigg( \dfrac{5}{3} \bigg)^{8x}$

To Find:

Value of x.

Solution:

$\sf \bigg( \dfrac{5}{3} \bigg)^{-5} \times  \bigg( \dfrac{5}{3} \bigg)^{-11} =  \bigg( \dfrac{5}{3} \bigg)^{8x}$

Using the law of exponents,

$\sf \implies a^m \times a^n = a^{m+n}$

$\sf \implies \bigg( \dfrac{5}{3} \bigg)^{(-5)+(-11)} = \bigg( \dfrac{5}{3} \bigg)^{8x}$

Adding the exponents,

$\sf \implies \bigg( \dfrac{5}{3} \bigg)^{-16} = \bigg( \dfrac{5}{3} \bigg)^{8x}$

Let's take the exponents,

$\sf \implies -16 = 8x$

Solving the equation,

$\sf \implies \dfrac{-16}{8} = x$

$\sf \implies -2 = x$

Verification:

To verify, let's substitute the value of x.

$\sf \bigg( \dfrac{5}{3} \bigg)^{-5} \times  \bigg( \dfrac{5}{3} \bigg)^{-11} =  \bigg( \dfrac{5}{3} \bigg)^{8x}$

Substitute the value of x,

$\sf \implies \bigg( \dfrac{5}{3} \bigg)^{-5} \times  \bigg( \dfrac{5}{3} \bigg)^{-11} =  \bigg( \dfrac{5}{3} \bigg)^{8\times (-2)}$

$\sf \implies (-5) + (-11) = 8 \times (-2)$

Solving the equation,

$\sf \implies -5-11 = 8 \times -2$

$\sf \implies -16 = 8 \times -2$

$\sf \implies -16 = -16$

∵ LHS = RHS

∴ Thus, verified.