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  1. Home
  2. 12th grade
  3. Algebra I
  4. Exercise : Convert a quotient of exponentials into a difference

Convert a quotient of exponentials into a difference Algebra I

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

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See also
  • Course : Exponential functions
  • Exercise : Match exponential functions and their graphs
  • Exercise : Convert between a product of exponentials and a sum
  • Exercise : Convert between exponentials with powers and a product of exponents
  • Exercise : Find a formula of exponential growth or decay from two points
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