Question

find the value of p in
$({2}^{3}) ^{4} = ({2}^{2}) ^{p}$
​

Answer 1

Answer:

Given :

$((2 ){}^{3} ) {}^{4} = (2 {}^{2} ) {}^{p}$

Formulae used :

$1) \: \: ((a) {}^{m} ) {}^{n} = a {}^{mn} \\ 2) \: \: a {}^{x} = a {}^{y} \\ x = y$

What to find out = value of P?

Solution :

$((2) {}^{3} ) {}^{4} = (2 {}^{2} ) {}^{p} \\ \\ 2 {}^{12} = 2 {}^{2p} \\ now \: compare \: the \: power \\ 2p = 12 \\ p = \frac{12}{2} \\ p = 2 \: \: \: answer$

So the value of P = 2

Some basic exponent rules:-

$1) \: \: a {}^{n} \times a {}^{m} = a {}^{n + m} \\ 2) \: \: \frac{a {}^{n} }{a {}^{m} } = a {}^{n - m} \\ 3) \: \: a {}^{0} = 1 \\ 4) \: \: 1 {}^{n} = 1 \\ 5) \: \: a {}^{ - n} = \frac{1}{a {}^{n} }$