3^4 x 4^2 = 4 – ?

Let’s tackle your questions one at a time!

1. For the equation (3^4 times 4^2 = 4 – ?):

– First, calculate (3^4 = 81) and (4^2 = 16). Then multiply:

[

81 times 16 = 1296

]

– Now we need to rewrite the equation:

[

1296 = 4 – x

]

– So, rearranging gives (x = 4 – 1296) which would be (x = -1292).

2. For the equation ((2^3)^4 = 2 – ?):

– Using the rule of powers, ((a^m)^n = a^{m cdot n}):

[

(2^3)^4 = 2^{3 cdot 4} = 2^{12}

]

– So we have (2^{12} = 2 – x).

– If we equate them, we find (x = 2 – 2^{12}) which is a large negative number.

3. The statement “The power of a power, multiply the exponents”:

– This rule states that when you have an exponent raised to another exponent, you multiply the exponents together. For