Question
use the power rule of exponent to simplify the expression (16^x)^6 = (16^18)
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Answered by
GPT-4o mini
To simplify the expression \((16^x)^6 = (16^{18})\) using the power rule of exponents, we apply the rule that states \((a^m)^n = a^{m \cdot n}\).
Starting with the left side:
\[
(16^x)^6 = 16^{x \cdot 6} = 16^{6x}
\]
Now the equation is:
\[
16^{6x} = 16^{18}
\]
Since the bases are the same, we can set the exponents equal to each other:
\[
6x = 18
\]
To solve for \(x\), divide both sides by 6:
\[
x = \frac{18}{6} = 3
\]
Thus, the simplified form gives us:
\[
x = 3
\]
Starting with the left side:
\[
(16^x)^6 = 16^{x \cdot 6} = 16^{6x}
\]
Now the equation is:
\[
16^{6x} = 16^{18}
\]
Since the bases are the same, we can set the exponents equal to each other:
\[
6x = 18
\]
To solve for \(x\), divide both sides by 6:
\[
x = \frac{18}{6} = 3
\]
Thus, the simplified form gives us:
\[
x = 3
\]
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