Question

if (-3)^(m+1)×(-3)^5=(-3)^7 then the value of m is

Answer 1

Answer :-

$\sf (-3)^{m+1} \times (-3)^5 = (-3)^7$

Using the property of exponents :-

• $\sf a^m \times a^n = a^{m+n}$

$\implies\sf (-3)^{m+1+5} = -3^7$

$\implies\sf (-3)^{m+6} = -3^7$

Now, here base are same. So, the power will also be same :-

$\implies\sf m + 6 = 7$

$\implies\sf m = 7 - 6$

$\implies\sf m = 1$

Verification :-

$\sf LHS = (-3)^{m+1} \times (-3)^5$

$\implies\sf LHS = (-3)^{1 + 1} \times (-3)^5$

$\implies\sf LHS = (-3)^2 \times (-3)^5$

$\implies\sf LHS = (-3)^{2+5}$

$\implies\sf LHS = (-3)^7$

$\sf RHS = (-3)^7$

LHS = RHS

Hence verified.

Additional information :-

$\bf{\dag}\:\:\underline{\text{Law of Exponents :}}$

$\bigstar\:\:\sf\dfrac{a^m}{a^n} = a^{m - n}$

$\bigstar\:\:\sf{(a^m)^n = a^{mn}}$

$\bigstar\:\:\sf(a^m)(a^n) = a^{m + n}$

$\bigstar\:\:\sf\dfrac{1}{a^n} = a^{-n}$

$\bigstar\:\:\sf\sqrt[\sf n]{\sf a} = (a)^{\dfrac{1}{n}}$

Answer 2

Answer:

GIVEN:

(-3)m + 1 × (-3)5 = (-3)7

TO FIND:

The value of m .

SOLUTION:

=> -3m + 1 × (-15) = (-3) × 7

=> -3m + ( -15 ) = -21

=> -3m -15 = -21

=> -3m = -21 + 15

=> -3m = -6

=> m = -6 / -3

=> m = 2

Hence,the value of m is 2