Question

plz explain step by step​

Answer 1

2

Step-by-step explanation:

Given:

${9}^{(p + 1)} \div {3}^{p} = 81$

To find:

The value of p

Point to be noted

1)Law of Indecis will be used

2) Break the exponents in smallest form i.e 9 = 3², 81 = 3⁴.

3) Split the variable and constant powers i.e $2^{2+x}= 2^2.2^x$. As required.

Solution:

${9}^{(p + 1)} \div {3}^{p} = 81 \\ \\ {3}^{2(p + 1)} \times \frac{1}{ {3}^{p} } = {3}^{4} \\ \\ {3}^{2p + 2} \times {3}^{ - p} = {3}^{4} \\ \\ {3}^{2p + 2 - p} = {3}^{4} \\ \\ {3}^{p + 2} = {3}^{4} \\ \\ [\text{Eliminating the base from both side}] \\ \\ p + 2= 4 \\ \\ p = 4 - 2 \\ \\p = 2$

The required value of p is 2 .

${\boxed{\pink{\text{ Some Important Laws of Indices}}}}$

${a}^{n}.{a}^{m}={a}^{(n + m)}$

${a}^{-1}=\dfrac{1}{a}$

$\dfrac{{a}^{n}}{ {a}^{m}}={a}^{(n-m)}$

${({a}^{c})}^{b}={a}^{b\times c}={a}^{bc}$

${a}^{\frac{1}{x}}=\sqrt[x]{a}$

$[\text{where all variables are real and greater than 0}]$