Evaluate the following to determine the value of (8to the third power )to the n power = 8 to thhe 12 power

Answer 1

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.