Which expression is equivalent to 2⋅26 ? Hint: What does the product rule of exponents tell us to do if the base is the same? (1 point) Responses 26 2 to the 6th power 12−7 the fraction with numerator 1 and denominator 2 to the negative 7 power 27 2 to the 7th power 25

Answer 1

To solve the problem, we can use the product rule of exponents, which states that if you multiply powers with the same base, you can add their exponents.

In this case, we can express \(2 \cdot 26\) as:

\[ 2 \cdot 2^6 \]

Here, \(26\) can be rewritten as \(2^6\) since \(2\) is the base with an exponent of \(6\).

Now applying the product rule:

\[ 2^1 \cdot 2^6 = 2^{1 + 6} = 2^7 \]

So \(2 \cdot 26\) is equivalent to \(2^7\).

From the provided responses, the one that matches this result is:

27 2 to the 7th power

So the equivalent expression is \(2^7\).