Answered

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Apply the product rule for exponents, if possible.

[tex]\[ g^{14} \cdot h^4 \][/tex]

A. [tex]\( gh^{10} \)[/tex]
B. [tex]\( gh^{18} \)[/tex]
C. [tex]\( g^{56}h \)[/tex]
D. The product rule does not apply.

Sagot :

GinnyAnswer
Let's analyze the given expression [tex]\( g^{14} \cdot h^4 \)[/tex].

The product rule for exponents states that when you multiply like bases, you add the exponents. In mathematical terms, for any bases [tex]\( a \)[/tex] and [tex]\( b \)[/tex] (where [tex]\( a = b \)[/tex]), and exponents [tex]\( m \)[/tex] and [tex]\( n \)[/tex]:
[tex]\[ a^m \cdot a^n = a^{m+n} \][/tex]

However, in the given expression, we have different bases: [tex]\( g \)[/tex] and [tex]\( h \)[/tex]. The bases are not the same, meaning that the product rule for exponents cannot be applied.

Thus, the correct answer is:
D. The product rule does not apply.
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