Answer :
To determine the greatest common factor (GCF) of [tex]\( h^4 \)[/tex] and [tex]\( h^8 \)[/tex], we need to look at the exponents of the common variable [tex]\( h \)[/tex].
1. The prime factorization of [tex]\( h^4 \)[/tex] is [tex]\( h \times h \times h \times h \)[/tex] (or [tex]\( h^4 \)[/tex]).
2. The prime factorization of [tex]\( h^8 \)[/tex] is [tex]\( h \times h \times h \times h \times h \times h \times h \times h \)[/tex] (or [tex]\( h^8 \)[/tex]).
The GCF of these terms involves finding the lowest power of [tex]\( h \)[/tex] that is common to both terms.
- For [tex]\( h^4 \)[/tex], the exponent is 4.
- For [tex]\( h^8 \)[/tex], the exponent is 8.
The greatest common factor will be [tex]\( h \)[/tex] raised to the lowest power of the exponents involved. Between 4 and 8, the lowest exponent is 4.
Thus, the GCF of [tex]\( h^4 \)[/tex] and [tex]\( h^8 \)[/tex] is [tex]\( h^4 \)[/tex].
Therefore, the answer is:
[tex]\[ h^4 \][/tex]
1. The prime factorization of [tex]\( h^4 \)[/tex] is [tex]\( h \times h \times h \times h \)[/tex] (or [tex]\( h^4 \)[/tex]).
2. The prime factorization of [tex]\( h^8 \)[/tex] is [tex]\( h \times h \times h \times h \times h \times h \times h \times h \)[/tex] (or [tex]\( h^8 \)[/tex]).
The GCF of these terms involves finding the lowest power of [tex]\( h \)[/tex] that is common to both terms.
- For [tex]\( h^4 \)[/tex], the exponent is 4.
- For [tex]\( h^8 \)[/tex], the exponent is 8.
The greatest common factor will be [tex]\( h \)[/tex] raised to the lowest power of the exponents involved. Between 4 and 8, the lowest exponent is 4.
Thus, the GCF of [tex]\( h^4 \)[/tex] and [tex]\( h^8 \)[/tex] is [tex]\( h^4 \)[/tex].
Therefore, the answer is:
[tex]\[ h^4 \][/tex]
