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Answer :
To simplify the expression [tex]\( 625x^4 \)[/tex] completely, we can follow these steps:
1. Understand Each Part of the Expression:
- We have a numerical coefficient, [tex]\(625\)[/tex].
- The variable part is [tex]\(x^4\)[/tex], which means [tex]\(x\)[/tex] raised to the fourth power.
2. Consider the Numerical Coefficient:
- The number [tex]\(625\)[/tex] can be expressed in a simpler form as a power of another number. In this case, [tex]\(625 = 5^4\)[/tex]. This is because [tex]\(5 \times 5 \times 5 \times 5 = 625\)[/tex].
3. Rewrite the Expression:
- Using the information above, we can rewrite the original expression [tex]\(625x^4\)[/tex] as [tex]\((5^4)x^4\)[/tex].
4. Combine the Powers:
- The expression [tex]\((5^4)x^4\)[/tex] can be combined as a single power since both parts are raised to the same exponent. So, it becomes [tex]\((5x)^4\)[/tex].
5. Final Simplified Expression:
- The completed simplification of the expression [tex]\(625x^4\)[/tex] is [tex]\((5x)^4\)[/tex].
And there you have it, the expression is simplified completely to [tex]\((5x)^4\)[/tex].
1. Understand Each Part of the Expression:
- We have a numerical coefficient, [tex]\(625\)[/tex].
- The variable part is [tex]\(x^4\)[/tex], which means [tex]\(x\)[/tex] raised to the fourth power.
2. Consider the Numerical Coefficient:
- The number [tex]\(625\)[/tex] can be expressed in a simpler form as a power of another number. In this case, [tex]\(625 = 5^4\)[/tex]. This is because [tex]\(5 \times 5 \times 5 \times 5 = 625\)[/tex].
3. Rewrite the Expression:
- Using the information above, we can rewrite the original expression [tex]\(625x^4\)[/tex] as [tex]\((5^4)x^4\)[/tex].
4. Combine the Powers:
- The expression [tex]\((5^4)x^4\)[/tex] can be combined as a single power since both parts are raised to the same exponent. So, it becomes [tex]\((5x)^4\)[/tex].
5. Final Simplified Expression:
- The completed simplification of the expression [tex]\(625x^4\)[/tex] is [tex]\((5x)^4\)[/tex].
And there you have it, the expression is simplified completely to [tex]\((5x)^4\)[/tex].
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