Answer: [tex]\frac{1}{h^{10} }[/tex]
Step-by-step explanation: Use the exponent rule [tex]x^{a}[/tex]·[tex]x^{b}[/tex]=[tex]x^{a+b}[/tex] (In other words, the exponents can be added because the bases are the same) to simplify the numerator:
[tex]\frac{h^{29} *h^{-39} }{h^{0} }[/tex]=[tex]\frac{h^{29+(-39)} }{h^{0} }[/tex]
Simplify the numerator:
[tex]\frac{h^{29+(-39)} }{h^{0} }[/tex]=[tex]\frac{h^{-10} }{h^{0} }[/tex]
Use the exponent rule [tex]\frac{x^{a} }{x^{b} } =x^{a-b}[/tex] (In other words, the exponents can be subtracted because the bases are the same) to simplify the remaining expression:
[tex]\frac{h^{-10} }{h^{0} }[/tex]=[tex]h^{-10-0}[/tex]=[tex]h^{-10}[/tex]
To make the exponent positive, put h in the denominator:
[tex]h^{-10} =\frac{1}{h^{10} }[/tex]
