Question

Find the value of m,
(6 to the power m × 6 to the power 3 × 6 to the power-2)/(6 to the power-5) = 6 to the power 12

Answer 1

Answer:

The question given to us is:

\frac{6^m}{6^{-3}}=6^5

6

−3

6

m

=6

5

This can be re-written as:

6^{m-(-3)}=6^56

m−(−3)

=6

5

(\since \frac{a^m}{a^n}=a^{m-n}\since

a

n

a

m

=a

m−n

)

Thus, we get:

6^{m+3}=6^56

m+3

=6

5

Now, comparing the exponents in the above equation, we will get:

m+3=5m+3=5

\therefore m=5-3=2∴m=5−3=2

Thus, the last option, option IV, m=2, is the correct option.

Step-by-step explanation:

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