Question

find the value of m in the following 3m×3^6/3^-³=3^18​

Answer 1

➤ Answer

• The value of m = 9.

➤ Given

• A equation $\tt\cfrac{{3}^{m} \times {3}^{6}}{ {3}^{ -3} } = {3}^{18}$.

➤ To Find

• The value of m.

➤ Step By Step Explanation

In this question we have given a equation $\tt\cfrac{{3}^{m} \times {3}^{6}}{ {3}^{ -3} } = {3}^{18}$. We need to find the value of m. We can find the value of m by using exponential identities and by basic arithmetic.

So let's do it !!

➵ Formula Used

• $\boxed{\tt{{a}^{m} \times {a}^{n} = {a}^{m + n}}}$

• $\boxed{ \tt{{a}^{- m} = \cfrac{1}{ {a}^{m} }}}$

• $\boxed{ \tt{\cfrac{ {a}^{m} }{ {a}^{n} } = {a}^{m - n}}}$

➵ Solution

$\longmapsto\tt\cfrac{ {3}^{m} \times {3}^{6} }{ {3}^{ - 3} } = {3}^{18} \\ \\ \longmapsto\tt\cfrac{ {3}^{m} \times {3}^{6}}{ \frac{1}{ {3}^{3}}} = {3}^{18} \\ \\ \longmapsto\tt {3}^{m} \times {3}^{6} \times {3}^{3} = {3}^{18} \\ \\\longmapsto\tt {3}^{m} \times {3}^{6 + 3} = {3}^{18} \\ \\ \longmapsto\tt {3}^{m} \times {3}^{9} = {3}^{18} \\ \\\longmapsto\tt {3}^{m} = \cfrac{ {3}^{18} }{ {3}^{9} } \\ \\ \longmapsto\tt {3}^{m} = {3}^{18 - 9} \\ \\\longmapsto\tt {3}^{m} = {3}^{9} \\ \\ \longmapsto\tt m = 9$

Therefore, the value of m = 9.

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➤ More to Know

${ \tt{Law \: of \: Exponents :}}\\\\\bigstar\:\:\sf\dfrac{a^m}{a^n} = a^{m - n}\\\\\bigstar\:\:\sf{(a^m)^n = a^{mn}}\\\\\bigstar\:\:\sf(a^m)(a^n) = a^{m + n}\\\\\bigstar\:\:\sf\dfrac{1}{a^n} = a^{-n}\\\\\bigstar\:\:\sf\sqrt[\sf n]{\sf a} = (a)^{\frac{1}{n}}$

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