Question

solve the question urgently a and b

Answer 1

$(a) \\ 25 \times (5^{\frac{1}{2}} ) ^{3} = 5^{p} \\ {5}^{2} \times 5 ^{ \frac{3}{2} } = 5 ^{p} \\ 5 ^{2 + \frac{3}{2} } =5 ^{p} \\ 5 ^{ \frac{4 + 3}{2} } = 5 ^{p} \\ 5 ^{\frac{7}{2}} = 5 ^{p} \\ p = \frac{7}{2} \\ \\ \\ \\ (b) \\ 8 \times (2 ^{ \frac{1}{3} } ) = 2 ^{3p} \\ {2}^{3 } \times 2 ^{ \frac{1}{3} } = 2 ^{3p} \\ 2 ^{3 + \frac{1}{3} } = 2 ^{3p} \\ 2 ^{ \frac{9 + 1}{3} } = 2 ^{3p} \\ 2 ^{ \frac{10}{3} } = 2 ^{3p} \\ \frac{10}{3} = 3p \\ p = \frac{10}{9}$