Answer:
[tex]y=\dfrac{10}{3}[/tex]
Step-by-step explanation:
[tex]\left(\dfrac25\right)^{-3} \cdot\left(\dfrac52\right)^{-15} =\left(\dfrac25\right)^{2+3y}[/tex]
[tex]\textsf{Using exponent rule:}\left(\dfrac{a}{b}\right)^{-c} =\left(\dfrac{b}{a}\right)^{c}[/tex]
[tex]\implies \left(\dfrac25\right)^{-3} \cdot\left(\dfrac25\right)^{15} =\left(\dfrac25\right)^{2+3y}[/tex]
[tex]\textsf{Using exponent rule: } a^b \cdot a^c=a^{b+c}[/tex]
[tex]\implies \left(\dfrac25\right)^{-3} \cdot\left(\dfrac25\right)^{15} =\left(\dfrac25}\right)^2 \cdot \left(\dfrac25\right)^{3y}[/tex]
[tex]\implies \left(\dfrac25\right)^{12} =\left(\dfrac25}\right)^2 \cdot \left(\dfrac25\right)^{3y}[/tex]
[tex]\implies \left(\dfrac25\right)^{12} \div\left(\dfrac25}\right)^2 =\left(\dfrac25\right)^{3y}[/tex]
[tex]\textsf{Using exponent rule: } \dfrac{a^b}{a^c}=a^{b-c}[/tex]
[tex]\implies \left(\dfrac25\right)^{10} =\left(\dfrac25\right)^{3y}[/tex]
[tex]\textsf{Using exponent rule: } a^b=a^c \implies b=c[/tex]
[tex]\implies 10=3y[/tex]
[tex]\implies y=\dfrac{10}{3}[/tex]
