Question

5^2m × 5 ^-4 = 5 ^16​

Answer 1

Given: The equation is$5^{2m} \times 5 ^{-4} = 5 ^{16}$.

We have to solve the above equation.

• As we know that from the Product of powers rule of exponent:
• When multiplying two bases of the same value, we have to keep the bases the same and then add the exponents together to get the solution.
• By using the above concept we are solving the above equation.

We are solving in the following way:

We have,

$5^{2m} \times 5 ^{-4} = 5 ^{16}$

$5^{2m+-4} =5^{16}\\\\5^{2m-4}=5^{16}$

Equating power of both the sides LHS and RHS:

$=>2m-4=16\\=>2m=16+4\\=>2m=20\\\\=>m=\frac{20}{2} \\\\=>m=10$

Hence, the solution of the above equation is$10$.