Question

Anyone know how to solve this? 64^-3m = 16^-2m-2

Answer 1

m = 4/5

Explanation:

Since 64 and 16 are both powers of 4, the first step is to change both sides of the equation to some power of 4.

64 is 4^3.

16 is 4^2.

see image.

Then use exponent rules to simplify. If you have a power to a power, multiply the exponents.

see image.

Then since the bases are the same, we can just work on the exponents. Yes, just kick those base 4 right out of the equation and set the exponents equal to each other. Solve the linear equation. It takes three steps. Distribute, combine like terms, divide. See image.