[tex]\displaystyle \sf{ If \: \: {5}^{x} = 100 \: then \: \: {5}^{x - 2} = \bf 4 }[/tex]
Correct question :
[tex]\displaystyle \sf{ If \: \: {5}^{x} = 100 \: then \: \: {5}^{x - 2} = ? }[/tex]
Given :
[tex]\displaystyle \sf{ {5}^{x} = 100 }[/tex]
To find :
[tex]\displaystyle \sf{ The \:value\: of \: \: {5}^{x - 2} }[/tex]
Formula :
We are aware of the formula on indices that
[tex] \displaystyle \sf{\frac{ {a}^{m} }{ {a}^{n} } = {a}^{m - n} }[/tex]
Solution :
Step 1 of 2 :
Write down the given equation
Here the given equation is
[tex]\displaystyle \sf{ {5}^{x} = 100 \: }[/tex]
Step 2 of 2 :
Find the required value
[tex]\displaystyle \sf{ {5}^{x - 2} }[/tex]
[tex]\displaystyle \sf{ = \frac{ {5}^{x} }{ {5}^{2} } }\: \: \: \bigg[ \: \because \:\frac{ {a}^{m} }{ {a}^{n} } = {a}^{m - n} \bigg] [/tex]
[tex]\displaystyle \sf{ = \frac{100}{25}\: \: \: \bigg[ \: \because \: {5}^{x} = 100 \bigg] }[/tex]
[tex]\displaystyle \sf{ } = 4[/tex]
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[tex]1.[/tex] choose the correct alternative : 100¹⁰⁰ is equal to (a) 2¹⁰⁰ × 50¹⁰⁰ (b) 2¹⁰⁰ + 50¹⁰⁰ (c) 2² × 50⁵⁰ (d) 2² + 50⁵⁰
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2. Using law of exponents, simplify (5²)³÷5³
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