Find the value of p in each of the following.....

1.	Find the value of p in each of the following.....
Answer» <P>ANSWER: (a) 3/2 (B) 7 Step-by-step EXPLANATION: (a) $7^{2p} \div 343 = 1$ $\dfrac{7^{2p} }{343} = 1$ $\dfrac{7^{2p} }{7^{3} } = 1$ $7^{2p-3} = 1$ $7^{2p-3} = 7^{0}$ $2p - 3 =0$ $2p = 3\\$ $p = \dfrac{3}{2}$ ∴ p = 3/2 (b) $(3^{p})^{3} \times 9^{2} \times 243^{-5} = 1$ $(3^{p})^{3} \times (3^{2})^{2} \times (3^5)^{-5} = 1$ $3^{3p} \times 3^{4} \times 3^{-25} = 1$ ${3^{3p+4+(-25)} = 1$ ${3^{3p+4-25} = 1$ ${3^{3p-21} = 1$ $3^{3p-21} = 3^0$ $3p-21 = 0$ $3p = 21$ $p = \dfrac{21}{3}$ $p = 7$ ∴ p = 7

Answer»

<P>ANSWER: (a) 3/2 (B) 7

Step-by-step EXPLANATION:

(a) $7^{2p} \div 343 = 1$