Question

8^2m x 8^1= 8^9
what is the value of m?

Answer 1

Solution:

» 8^2m × 8¹ = 8⁹

» 8^2m = 8⁸

On equating, we get

» 2m = 8

» m = 4

Therefore, the value of m is 4.

Answer 2

Answer :

• Value of m is 4

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Given :

• $\sf {8}^{2m} \times {8}^{1} \:=\: {8}^{9}$

To Find :

• Value of m

Solution :

Here , we will use following two properties :

1. $\sf \dfrac{{a}^{m}}{{a}^{n}} \:=\: {a}^{m\:-\:n}$
2. $\sf {a}^{m} \:=\: {a}^{n} \:then\:m\:=\:n$

$\implies\sf {8}^{2m} \times {8}^{1} \:=\: {8}^{9}$

$\implies \sf {8}^{2m} \:=\: \dfrac{{8}^{9}}{{8}^{1}}$

$\implies \sf {8}^{2m} \:=\: {8}^{9\:-\:1}$

$\implies \sf {8}^{2m} \:=\: {8}^{8}$

• Now , since bases are equal , power can be equated .

$\implies \sf 2m \:=\: 8$

$\implies \sf m \:=\: \dfrac{8}{2}$

$\implies \sf m\:=\: 4$

• Value of m is 4

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