Question

If (2/3)^6 × (9/4)^5 = (3/2)^m+2 , then find the value of *m*
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please answer!​

Answer 1

Step-by-step explanation:

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Answer 2

Concept

If the bases of two equal numbers are equal, then their powers must be same. For example, if (a)^b = (a)^c, the b and c must be equal.

Given

an expression (2/3)^6 × (9/4)^5 = (3/2)^m+2

Find

we need to find the value of m

Solution

We have

(2/3)^6 × (9/4)^5 = (3/2)^m+2

we can rewrite the equation as

(2/3)^6 × (3/2)^10 = (3/2)^m+2

after cancelling out the common terms we will be left with

(3/2)^4 = (3/2)^m+2

now since the bases on both sides are equal, the powers will be equal

4 = m+2

m = 2

Thus, the value of m is 2.

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