Rewrite each of the following in the form of a single exponential. $$ \begin{array}{lll} ext { (a) } 6^{23} \cdot 6^{15} & ext { (b) }\left(5^{2} ight)^{4} & ext { (c) } x^{6} \cdot z^{6}\end{array} $$ (a) $$ 6^{23} \cdot 6^{15}=\square $$ (Type your answer using exponential notation.)

Question

Rewrite each of the following in the form of a single exponential. $$ \begin{array}{lll}	ext { (a) } 6^{23} \cdot 6^{15} & 	ext { (b) }\left(5^{2}ight)^{4} & 	ext { (c) } x^{6} \cdot z^{6}\end{array} $$ (a) $$ 6^{23} \cdot 6^{15}=\square $$ (Type your answer using exponential notation.)

UpStudy AI · Accepted Answer

1. Recognize that when multiplying expressions with the same base, you add their exponents:
   $$
   a^m \cdot a^n = a^{m+n}
   $$

2. Apply this rule to the given expression:
   $$
   6^{23} \cdot 6^{15} = 6^{23+15}
   $$

3. Compute the sum of the exponents:
   $$
   23+15 = 38
   $$

4. Write the final expression:
   $$
   6^{38}
   $$

Thus, the answer is:
$$
6^{38}
$$
$$ 6^{38} $$

Rewrite each of the following in the form of a single exponential. \( \begin{array}{lll}\text { (a) } 6^{23} \cdot 6^{15} & \text { (b) }\left(5^{2}\right)^{4} & \text { (c) } x^{6} \cdot z^{6}\end{array} \) (a) \( 6^{23} \cdot 6^{15}=\square \) (Type your answer using exponential notation.)

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