GabiK271918 GabiK271918
  • 25-10-2022
  • Mathematics
contestada

7^2 × 7^8. 7^a------------ = -------- = 7^b7^4 7^4

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BrayliI129462 BrayliI129462
  • 25-10-2022

We have to find the values of a and b:

[tex]\frac{7^2\cdot7^8}{7^4}=\frac{7^a}{7^4}=7^b[/tex]

We can use the laws of exponents to write:

[tex]\begin{gathered} 7^2\cdot7^8=7^a \\ 7^{2+8}=7^a \\ 7^{10}=7^a \\ 10=a \end{gathered}[/tex]

Then, we can solve for b as:

[tex]\begin{gathered} \frac{7^a}{7^4}=7^b \\ 7^{a-4}=7^b \\ a-4=b \\ 10-4=b \\ 6=b \end{gathered}[/tex]

Answer: a=10 and b=6

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