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  1. Home
  2. 12th grade
  3. Precalculus
  4. Exercise : Convert between a product of exponentials and a sum

Convert between a product of exponentials and a sum Precalculus

The following exponential forms are equal to another one. Pick the right answer.

\left( \dfrac35 \right)^{2+x}

If a, b and c are three real numbers with c\gt0, then:

c^{a+b}=c^a\times c^b

Therefore:

\left( \dfrac35 \right)^{2+x} = \left( \dfrac35 \right)^{2} \left( \dfrac35 \right)^{x}

\left( \dfrac35 \right)^{2+x} =\left( \dfrac{3^2} {5^2} \right) \left( \dfrac35 \right)^{x}

\left( \dfrac35 \right)^{2+x} =\dfrac{9}{25} \left( \dfrac{3}{5} \right)^x

3^3 \times 3^{x}

If a, b and c are three real numbers with c\gt0, then:

c^a\times c^b=c^{a+b}

Therefore:

3^3 \times 3^x =3^{3+x}

a^5 \times a^{-2}

If a, b and c are three real numbers with c\gt0, then:

c^a\times c^b=c^{a+b}

Therefore:

a^5 \times a^{-2} =a^{5+\left(-2\right)}

a^5 \times a^{-2} =a^{5-2}

a^5 \times a^{-2} =a^{3}

2^{x+5}

If a, b and c are three real numbers with c\gt0, then:

c^{a+b}=c^a\times c^b

Therefore:

2^{x+5}=2^x \times 2^5

2^{x+5}=2^x \times 32

a^2 \times a^{3}

If a, b and c are three real numbers with c\gt0, then:

c^a\times c^b=c^{a+b}

Therefore:

a^2 \times a^{3}=a^{2+3}

a^2 \times a^{3}=a^5

6^{2+x}

If a, b and c are three real numbers with c\gt0, then:

c^{a+b}=c^a\times c^b

Therefore

6^{2+x} =6^2 \times 6^x

6^{2+x}=36 \times 6^x

2^{3+6}

If a, b and c are three real numbers with c\gt0, then:

c^{a+b} =c^a\times c^b

Therefore:

2^{3+6}=2^{3}\times 2^6

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See also
  • Course : Exponential functions
  • Exercise : Match exponential functions and their graphs
  • Exercise : Convert a quotient of exponentials into a difference
  • 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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