Evaluate the following to determine the value of (8to the third power )to the n power = 8 to thhe 12 power
To evaluate (8 to the third power) to the n power, we need to multiply the exponents.
(8 to the third power) can be written as 8^3.
So, we have (8^3)^n.
Using the exponent property of raising a power to a power, we can simplify this expression by multiplying the exponents:
(8^3)^n = 8^(3n).
Therefore, the value of (8 to the third power) to the n power is 8^(3n).
To determine the value of 8 to the twelfth power (8^12), simply substitute n = 4 into the expression 8^(3n):
8^(3n) = 8^(3*4) = 8^12.
Hence, the value of (8 to the third power) to the n power is equal to 8 to the twelfth power.