Question

if 10^3x =125 then find 10^-2x​

Answer 1

Step-by-step explanation:

Above are the steps to solve this question

Answer 2

Answer:

The value of  10⁻²ˣ is $\frac{1}{25}$

Step-by-step explanation:

Given that 10³ˣ = 125

We need to find 10⁻²ˣ

As we know that 5³ = 125,

we can write 10³ˣ = 125

=>                   10³ˣ = 5³

As(xᵃ)ᵇ = xᵃᵇ, therefore,

=>                   (10ˣ)³ = 5³

Taking cube root both sides

=>                   10ˣ = 5

As we need 10⁻²ˣ,

Therefore, raising both the sides to the power -2

=>                   10⁻²ˣ = 5⁻²

As we know that (x)⁻ᵃ = $\frac{1}{x^{a}}$

=>                   10⁻²ˣ = $\frac{1}{5^{2}}$

=>                   10⁻²ˣ = $\frac{1}{25}$

Therefore, the value of  10⁻²ˣ is $\frac{1}{25}$