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Which of the following expressions is equivalent to the one shown below?

[tex]\[ \frac{7^{13}}{7} \][/tex]

A. [tex]\( 7^{20} \)[/tex]

B. [tex]\( 7^5 \)[/tex]

C. [tex]\( 7^{91} \)[/tex]

D. [tex]\( 7^6 \)[/tex]

Sagot :

GinnyAnswer
To solve the given expression [tex]\(\frac{7^{13}}{7}\)[/tex], we can use the laws of exponents. Specifically, we will use the rule that states:

[tex]\[ \frac{a^m}{a^n} = a^{m-n} \][/tex]

Here, [tex]\(a\)[/tex] is the base (which is 7 in our case), [tex]\(m\)[/tex] is the exponent in the numerator (which is 13), and [tex]\(n\)[/tex] is the exponent in the denominator (which is 1, since [tex]\(7\)[/tex] can be written as [tex]\(7^1\)[/tex]).

Applying the rule:

[tex]\[ \frac{7^{13}}{7} = \frac{7^{13}}{7^1} = 7^{13-1} = 7^{12} \][/tex]

So, the expression [tex]\(\frac{7^{13}}{7}\)[/tex] simplifies to [tex]\(7^{12}\)[/tex].

The equivalent expression to [tex]\(7^{12}\)[/tex] is not directly listed in the given options (A: [tex]\(7^{20}\)[/tex], B: [tex]\(7^5\)[/tex], C: [tex]\(7^{91}\)[/tex], D: [tex]\(7^6\)[/tex]). Therefore, it appears that the correct simplified form of the expression does not match any of the provided choices.

However, the simplified expression is:

[tex]\[ 7^{12} \][/tex]

The equivalent numerical value here, coming from the simplified exponent, is [tex]\(12\)[/tex].
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