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Simplify. Rewrite the expression in the form [tex]$5^n$[/tex].

[tex]\left(5^3\right)^2 =[/tex]

[tex]\square[/tex]


Sagot :

To simplify the expression \(\left(5^3\right)^2\) and rewrite it in the form \(5^n\), we will follow a detailed, step-by-step approach.

1. Understand the Expression:
\(\left(5^3\right)^2\) means that we are raising \(5^3\) to the power of 2.

2. Apply the Power of a Power Rule:
The power of a power rule states that \((a^m)^n = a^{m \cdot n}\). Here, \(a = 5\), \(m = 3\), and \(n = 2\).

3. Multiply the Exponents:
Following the rule \((a^m)^n = a^{m \cdot n}\), we have:
[tex]\[ (5^3)^2 = 5^{3 \cdot 2} \][/tex]
Calculate the multiplication of the exponents:
[tex]\[ 3 \cdot 2 = 6 \][/tex]

4. Rewrite the Expression:
Replace the exponent with the calculated value:
[tex]\[ (5^3)^2 = 5^6 \][/tex]

So, the simplified form of the expression \(\left(5^3\right)^2\) rewritten in the form \(5^n\) is \(5^6\).

To express the value:
[tex]\[ 5^6 = 15625 \][/tex]

Final answer:
[tex]\[ \left(5^3\right)^2 = 5^6 = 15625 \][/tex]