Answer: [tex]\boldsymbol{2.376 \times 10^4}[/tex]
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Explanation:
Let's solve for 'a' in the original equation. Each x shown below indicates multiplication.
[tex](a \times 10^4)+(a \times 10^2) = 24240\\\\a(10^4+10^2) = 24240\\\\a(10000+100) = 24240\\\\a(10100) = 24240\\\\a = 24240/10100\\\\a = 2.4[/tex]
I used the distributive property to factor out the 'a' in the second step.
As a check so far,
[tex](a \times 10^4)+(a \times 10^2) = (2.4 \times 10^4)+(2.4 \times 10^2) = (24000)+(240) = 24240 \checkmark[/tex]
which shows we have the correct value for 'a'.
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Once we determine the value of 'a', we can compute the expression your teacher wants.
[tex](a \times 10^4)-(a \times 10^2)\\\\(2.4 \times 10^4)-(2.4 \times 10^2)\\\\(24000)-(240)\\\\23760\\\\\boldsymbol{2.376 \times 10^4}[/tex]
