Answer with positive exponent = [tex]\left(\frac{1}{5}\right)^3[/tex] or [tex]\frac{1}{5^3}[/tex]
Answer with negative exponent = [tex]5^{-3}[/tex]
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Explanation:
The rule we use is
[tex]a^b*a^c = a^{b+c}[/tex]
If we multiply two exponential expressions with the same base, then we add the exponents.
The base for each is 5. The exponents 4 and -7 add to -3.
This means
[tex]5^4*5^{-7} = 5^{4+(-7)} = 5^{-3}[/tex]
To convert to a positive exponent, we apply the reciprocal to the base. We go from 5, aka 5/1, to 1/5.
So, [tex]5^{-3} = \left(\frac{1}{5}\right)^3 = \frac{1^3}{5^3} = \frac{1}{5^3}[/tex]
