Answer :
To rewrite the expression [tex]\(\left(12^2\right)^{10}\)[/tex] as 12 to a single power, we can use the power rule of exponents. The power rule states that [tex]\((a^m)^n = a^{m \cdot n}\)[/tex].
Here, our base [tex]\(a\)[/tex] is 12, the exponent [tex]\(m\)[/tex] is 2, and the exponent [tex]\(n\)[/tex] is 10. We apply the power rule to combine the exponents:
[tex]\[ (12^2)^{10} = 12^{2 \cdot 10} \][/tex]
Now, we multiply the exponents:
[tex]\[ 2 \cdot 10 = 20 \][/tex]
Thus, the expression [tex]\((12^2)^{10}\)[/tex] can be rewritten as:
[tex]\[ 12^{20} \][/tex]
So, the expression [tex]\(\left(12^2\right)^{10} = 12^{20}\)[/tex].
Here, our base [tex]\(a\)[/tex] is 12, the exponent [tex]\(m\)[/tex] is 2, and the exponent [tex]\(n\)[/tex] is 10. We apply the power rule to combine the exponents:
[tex]\[ (12^2)^{10} = 12^{2 \cdot 10} \][/tex]
Now, we multiply the exponents:
[tex]\[ 2 \cdot 10 = 20 \][/tex]
Thus, the expression [tex]\((12^2)^{10}\)[/tex] can be rewritten as:
[tex]\[ 12^{20} \][/tex]
So, the expression [tex]\(\left(12^2\right)^{10} = 12^{20}\)[/tex].
