Question

Match the following provided that $a$ and $b$ any two rational numbers different from zero and $x,y$ are any two rational numbers.

$\left(1\right)$	$a^x\times a^y$	$\left(a\right)$	$a^{x-y}$
$\left(2\right)$	$a^x÷a^y$	$\left(b\right)$	$a^{xy}$
$\left(3\right)$	$(a^x{)}^y$	$\left(c\right)$	$a^{x+y}$
$\left(4\right)$	$(ab{)}^x$	$\left(d\right)$	$\frac{a^x}{b^x}$
$\left(5\right)$	${\left(\frac{a}{b}\right)}^x$	$\left(e\right)$	$a^x\times b^x$

• A. $1-\left(c\right),2-\left(a\right),3-\left(b\right),4-\left(e\right),5-\left(d\right)$
• B. $1-\left(b\right),2-\left(c\right),3-\left(a\right),4-\left(e\right),5-\left(d\right)$
• C. $1-\left(a\right),2-\left(c\right),3-\left(d\right),4-\left(e\right),5-\left(b\right)$
• D. $1-\left(a\right),2-\left(b\right),3-\left(c\right),4-\left(d\right),5-\left(e\right)$

Answer 1

The correct option is A $1-\left(c\right),2-\left(a\right),3-\left(b\right),4-\left(e\right),5-\left(d\right)$

(1) If base is same then the product of two exponential numbers is same as base raised to the power equal to sum of exponents of each.

$\therefore a^x\times a^y=a^{x+y}$

(2) If base is same then the division of two exponential numbers is same as base raised to the power equal to difference of exponents of each.

$\therefore a^x÷a^y=a^{x-y}$

(3) $(a^x{)}^y=a^{xy}$

(4) $(ab{)}^x=(a^x{b}^x)=a^x\times b^x$

(5) $(\frac{a}{b}{)}^x=a^x÷b^x=\frac{a^x}{b^x}$