Question
Why can’t you use the product of powers rule to simplify this expression? Explain.
34 · 28
Answers
GPT-4o mini
The product of powers rule states that when you multiply two expressions with the same base, you can add their exponents. This rule can be expressed as:
\[
a^m \cdot a^n = a^{m+n}
\]
However, in the expression \(34 \cdot 28\), you are not working with powers that share the same base; instead, you are dealing with two distinct numbers (34 and 28) that are not written in exponential form.
To apply the product of powers rule, both terms must be powers of the same base, such as \(2^m\) and \(2^n\), or \(x^a\) and \(x^b\). Since 34 and 28 are simply integers, the product of powers rule does not apply here, and you cannot simplify the expression in that manner.
In summary, you cannot use the product of powers rule on \(34 \cdot 28\) because the multiplication involves two different numbers rather than powers of the same base.
\[
a^m \cdot a^n = a^{m+n}
\]
However, in the expression \(34 \cdot 28\), you are not working with powers that share the same base; instead, you are dealing with two distinct numbers (34 and 28) that are not written in exponential form.
To apply the product of powers rule, both terms must be powers of the same base, such as \(2^m\) and \(2^n\), or \(x^a\) and \(x^b\). Since 34 and 28 are simply integers, the product of powers rule does not apply here, and you cannot simplify the expression in that manner.
In summary, you cannot use the product of powers rule on \(34 \cdot 28\) because the multiplication involves two different numbers rather than powers of the same base.