Question

Simplify the expression (x to the 12 power) to the 3 power

Answer 1

Explanation:

To simplify this, I can think in terms of what those exponents mean. "To the third" means "multiplying three copies" and "to the fourth" means "multiplying four copies". Using this fact, I can "expand" the two factors, and then work backwards to the simplified form. First, I expand:

(x3)(x4) = (x‍x‍x)(x‍x‍x‍x)

Now I can remove the parentheses and put all the factors together:

(x‍x‍x)(x‍x‍x‍x) = x‍x‍x‍x‍x‍x‍x

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This is seven copies of the variable. "Multiplying seven copies" means "to the seventh power", so this can be restated as:

x‍x‍x‍x‍x‍x‍x = x7