Rewrite the following using a single exponent.
a^7b^7 = (____)----
(ab)^7
In order to rewrite the expression a^7b^7 using a single exponent, we can use the property of exponents known as the power of a product rule. This rule states that when we have a product raised to a power, we can distribute the exponent to each term within the parentheses. Let's apply this rule to rewrite the expression:
a^7b^7 = (a * a * a * a * a * a * a)(b * b * b * b * b * b * b)
Now, we can see that we have a product of the same variable, a, repeated seven times, and the same for variable b. To express this more concisely, we can write the expression using a single exponent:
(a * a * a * a * a * a * a)(b * b * b * b * b * b * b) = (a * b)^7
Therefore, the expression a^7b^7 can be rewritten as (a * b)^7.