Apply the Product Rule of Exponents to form an equivalent expression of 1^6⋅1^2⋅1^1

Answer 1

To apply the Product Rule of Exponents, we use the rule that states:

\[ a^m \cdot a^n = a^{m+n} \]

In your case, we have the expression:

\[ 1^6 \cdot 1^2 \cdot 1^1 \]

Since the base is the same (which is 1), we can add the exponents:

\[ 1^{6+2+1} = 1^{9} \]

Thus, the equivalent expression of \( 1^6 \cdot 1^2 \cdot 1^1 \) is:

\[ 1^9 \]

And since any power of 1 is still 1, we can also say:

\[ 1^{9} = 1 \]

So, the final result is:

\[ 1 \]

Answer 2

wrong pick one of these answers: 1^12 1^13 1^9 1^3

Answer 3

Let's evaluate the expression \( 1^6 \cdot 1^2 \cdot 1^1 \) again using the Product Rule of Exponents.

We add the exponents:

\[ 1^6 \cdot 1^2 \cdot 1^1 = 1^{6+2+1} = 1^9 \]

So, among the choices you provided, the correct answer is:

\[ \boxed{1^9} \]