Question

Steven claims that when you multiply two powers with the same base, the new exponent is the product of the original exponents. He uses the example below to support his claim.
3^2*3^2=3^(2.2)=3^4



3^__ *3^__=3^__

Answer 1

Steven's claim is incorrect in its presentation. The correct rule states that when you multiply two powers with the same base, you **add** the exponents, not multiply them.

The correct formula is:

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

So, for your example:

\[
3^2 \cdot 3^2 = 3^{2+2} = 3^4
\]

Now, let’s apply this to your blank format:

If we use the same exponents:
\[
3^2 \cdot 3^2 = 3^{2+2} = 3^4
\]

If you want to express it in the format you provided:
\[
3^x \cdot 3^y = 3^{x+y}
\]

You could fill in the blanks like this:
\[
3^2 \cdot 3^2 = 3^4
\]

or more generically with variables:
\[
3^x \cdot 3^y = 3^{x+y}
\]

Make sure to use addition, not multiplication, when combining exponents for powers with the same base.