Question

Pls ans this.....i will mark brainliest.​

Answer 1

Answer:

10/3

Step-by-step explanation:

( 5/2 )^-15 can also be written as ( 2/5 )^15.

So,

( 2/5 )^-3 x ( 2/5 )^15 = ( 2/5 )^( 2 + 3y )

Formulas : -

1. a^m x a^n = a^c

2. a^m x a^n = a^( m + n )

3. a^( m + n ) = a^c

Here ( m + n ) and c are powers.

a is the base.

Since bases are same on both sides, their powers are also same,

so m + n = c.

Here,

a = 2/5

m = - 3

n = 15

c = 2 + 3y

Substitute the values of m, n & c in " m + n = c ",

m + n = c

- 3 + 15 = 2 + 3y

15 - 3 = 2 + 3y

12 = 2 + 3y

12 - 2 = 3y

10 = 3y

y = 10/3

Answer 2

Answer:

$y=\dfrac{10}{3}$

Step-by-step explanation:

$\left(\dfrac25\right)^{-3} \cdot\left(\dfrac52\right)^{-15} =\left(\dfrac25\right)^{2+3y}$

$\textsf{Using exponent rule:}\left(\dfrac{a}{b}\right)^{-c} =\left(\dfrac{b}{a}\right)^{c}$

$\implies \left(\dfrac25\right)^{-3} \cdot\left(\dfrac25\right)^{15} =\left(\dfrac25\right)^{2+3y}$

$\textsf{Using exponent rule: } a^b \cdot a^c=a^{b+c}$

$\implies \left(\dfrac25\right)^{-3} \cdot\left(\dfrac25\right)^{15} =\left(\dfrac25}\right)^2 \cdot \left(\dfrac25\right)^{3y}$

$\implies \left(\dfrac25\right)^{12} =\left(\dfrac25}\right)^2 \cdot \left(\dfrac25\right)^{3y}$

$\implies \left(\dfrac25\right)^{12} \div\left(\dfrac25}\right)^2 =\left(\dfrac25\right)^{3y}$

$\textsf{Using exponent rule: } \dfrac{a^b}{a^c}=a^{b-c}$

$\implies \left(\dfrac25\right)^{10} =\left(\dfrac25\right)^{3y}$

$\textsf{Using exponent rule: } a^b=a^c \implies b=c$

$\implies 10=3y$

$\implies y=\dfrac{10}{3}$