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Answer :
To solve the expression [tex]\(2 \cdot 5^{x+1} - 625\)[/tex], we want to simplify it as much as possible. Here's how you can do that step-by-step:
1. Understand the Expression: The expression we have is [tex]\(2 \cdot 5^{x+1} - 625\)[/tex].
2. Rewrite the Expression: Start by expanding the exponent:
- [tex]\(5^{x+1}\)[/tex] can be rewritten using the properties of exponents as [tex]\(5^x \times 5^1\)[/tex], which is equal to [tex]\(5 \cdot 5^x\)[/tex].
3. Substitute Back into the Expression:
- Replace [tex]\(5^{x+1}\)[/tex] in the original expression with [tex]\(5 \cdot 5^x\)[/tex]:
[tex]\[
2 \cdot (5 \cdot 5^x) - 625
\][/tex]
4. Simplify the Expression:
- Carry out the multiplication:
[tex]\[
2 \cdot 5 \cdot 5^x = 10 \cdot 5^x
\][/tex]
- Now the expression becomes:
[tex]\[
10 \cdot 5^x - 625
\][/tex]
5. Final Simplified Expression:
- The simplified form of the given expression is [tex]\(10 \cdot 5^x - 625\)[/tex].
This is the step-by-step simplification of the expression [tex]\(2 \cdot 5^{x+1} - 625\)[/tex], resulting in [tex]\(10 \cdot 5^x - 625\)[/tex].
1. Understand the Expression: The expression we have is [tex]\(2 \cdot 5^{x+1} - 625\)[/tex].
2. Rewrite the Expression: Start by expanding the exponent:
- [tex]\(5^{x+1}\)[/tex] can be rewritten using the properties of exponents as [tex]\(5^x \times 5^1\)[/tex], which is equal to [tex]\(5 \cdot 5^x\)[/tex].
3. Substitute Back into the Expression:
- Replace [tex]\(5^{x+1}\)[/tex] in the original expression with [tex]\(5 \cdot 5^x\)[/tex]:
[tex]\[
2 \cdot (5 \cdot 5^x) - 625
\][/tex]
4. Simplify the Expression:
- Carry out the multiplication:
[tex]\[
2 \cdot 5 \cdot 5^x = 10 \cdot 5^x
\][/tex]
- Now the expression becomes:
[tex]\[
10 \cdot 5^x - 625
\][/tex]
5. Final Simplified Expression:
- The simplified form of the given expression is [tex]\(10 \cdot 5^x - 625\)[/tex].
This is the step-by-step simplification of the expression [tex]\(2 \cdot 5^{x+1} - 625\)[/tex], resulting in [tex]\(10 \cdot 5^x - 625\)[/tex].
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