Find the value of $$ p $$ when $$ 6^{p} imes 6^{4}=6^{28} $$

Question

Find the value of $$ p $$ when $$ 6^{p} 	imes 6^{4}=6^{28} $$

UpStudy AI · Accepted Answer

1. Start with the equation:  
   $$
   6^{p} \times 6^{4} = 6^{28}
   $$

2. Use the exponent property $$ a^{m} \times a^{n} = a^{m+n} $$ to combine the left-hand side:  
   $$
   6^{p+4} = 6^{28}
   $$

3. Since the bases are the same, set the exponents equal to each other:  
   $$
   p + 4 = 28
   $$

4. Solve for $$ p $$:  
   $$
   p = 28 - 4 = 24
   $$

5. Therefore, the value of $$ p $$ is:  
   $$
   p = 24
   $$
$$ p = 24 $$

Find the value of \( p \) when \( 6^{p} \times 6^{4}=6^{28} \)