If 5 power x=100 so 5powerx-2?

Answers 2

Answer:

Step-by-step explanation:

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[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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