The following exponential forms are equal to another one. Choose the right answer.
2^{x-3}
If a, b and c are three real numbers with c\gt0, then:
c^{a-b}=\dfrac{c^a}{c^b}
Therefore:
2^{x-3}=\dfrac{2^ x}{2^3}
2^{x-3}=\dfrac{2^x}{2 \times 2 \times 2 }
2^{x-3}=\dfrac{2^x}{8}
\dfrac{3^a}{3^{a+1}}
If a, b and c are three real numbers with c\gt0, then:
\dfrac{c^a}{c^b}=c^{a-b}
Therefore:
\dfrac{3^a}{3^{a+1}} = 3^{\left(a - \left(a+1\right)\right)}
\dfrac{3^a}{3^{a+1}} = 3^{\left(a-a-1\right)}
\dfrac{3^a}{3^{a+1}} =3^{-1}
\dfrac{3^a}{3^{a+1}} = \dfrac{1}{3}
\dfrac{2^5}{2^{7}}
If a, b and c are three real numbers with c\gt0, then:
\dfrac{c^a}{c^b}=c^{a-b}
Therefore:
\dfrac{2^5}{2^{7}}= 2^{\left(5 - 7\right)}=2^{-2}=\dfrac{1}{2^2}
\dfrac{2^5}{2^7}=\dfrac{1}{4}
\dfrac{5^6}{5^3}
If a, b and c are three real numbers with c\gt0, then:
\dfrac{c^a}{c^b}=c^{a-b}
Therefore:
\dfrac{5^6}{5^3} =5^{\left(6-3\right)}
\dfrac{5^6}{5^3}=5^3
2^{5-a}
If a, b and c are three real numbers with c\gt0, then:
c^{a-b}=\dfrac{c^a}{c^b}
Therefore:
{2^{5-a}}=\dfrac{{2^{5}}}{{2^{a}}}
{2^{5-a}}=\dfrac{32}{2^a}
\dfrac{5^8}{5^{4}}
If a, b and c are three real numbers with c\gt0, then:
\dfrac{c^a}{c^b}=c^{a-b}
Therefore:
\dfrac{5^8}{5^{4}} =5^{8-4}
\dfrac{5^8}{5^{4}}=5^4