Question

Match column I with column II and select the correct answer by using the given codes.

Column I Column II
$\left(A\right)3^4\times 3^{\frac{1}{2}}\left(P\right)7^{\frac{20}{7}}$
$\left(B\right)7^3\times 7^{-\frac{1}{7}}\left(Q\right)3^{\frac{21}{5}}$
$\left(C\right)3^4\times 3^{\frac{1}{5}}\left(R\right)5^{\frac{-7}{2}}$
$\left(D\right)5^{-\frac{1}{2}}\times 5^{-3}\left(S\right)3^{\frac{9}{2}}$

• A. $\left(A\right)\to \left(R\right)$, $\left(B\right)\to \left(Q\right)$, $\left(C\right)\to \left(S\right)$, $\left(D\right)\to \left(P\right)$
• B. $\left(A\right)\to \left(R\right)$, $\left(B\right)\to \left(P\right)$, $\left(C\right)\to \left(S\right)$, $\left(D\right)\to \left(Q\right)$
• C. $\left(A\right)\to \left(S\right)$, $\left(B\right)\to \left(P\right)$, $\left(C\right)\to \left(Q\right)$, $\left(D\right)\to \left(R\right)$
• D. $\left(A\right)\to \left(Q\right)$, $\left(B\right)\to \left(S\right)$,
  $\left(C\right)\to \left(P\right)$, $\left(D\right)\to \left(R\right)$

Answer 1

The correct option is C $\left(A\right)\to \left(S\right)$, $\left(B\right)\to \left(P\right)$, $\left(C\right)\to \left(Q\right)$, $\left(D\right)\to \left(R\right)$

Note: $a^m\times a^n=a^{m+n}$
So,
$\bullet 3^4\times 3^{\frac{1}{2}}$
$=3^{(4+\frac{1}{2})}$
$=3^{\frac{9}{2}}$

$\bullet 7^3\times 7^{-\frac{1}{7}}$
$=7^{(3-\frac{1}{7})}$
$=7^{\frac{20}{7}}$

$\bullet 3^4\times 3^{\frac{1}{5}}$
$=3^{(4+\frac{1}{5})}$
$=3^{\frac{21}{5}}$

$\bullet 5^{-\frac{1}{2}}\times 5^{-3}$
$=5^{(-\frac{1}{2}-3)}$
$=5^{-\frac{7}{2}}$