Question

(9/5) ⁷ ÷ (9/5) ² = (9/5) ²a-1

Answer 1

\(\left(\dfrac{9}{5}\right)^7:\left(\dfrac{9}{5}\right)^2=\left(\dfrac{9}{5}\right)^2a-1\)

\(\Leftrightarrow a\cdot\dfrac{81}{25}-1=\left(\dfrac{9}{5}\right)^5\)

\(\Leftrightarrow a\cdot\dfrac{81}{25}=\dfrac{59049}{3125}+1=\dfrac{62174}{3125}\)

\(\Leftrightarrow a=\dfrac{686}{1125}\)

Answer 2

=a⋅8125−1=(95)5⇔a⋅8125−1=(95)5

=a=6861125

Answer 3

\(\left(\dfrac{9}{5}\right)^7:\left(\dfrac{9}{5}\right)^2=\left(\dfrac{9}{5}\right)^{2a-1}\)

⇒\(\left(\dfrac{9}{5}\right)^5=\left(\dfrac{9}{5}\right)^{2a-1}\)

⇒5=2a-1

⇒2a=6

⇒a=3