Question

Answer This question

Answer 1

1)

a=3

2)

`(1)/(27)`

Explanation:

Use the property of exponent,
`a^m\cdot a^n=a^(m+n)`

`\left((2)/(3)\right)^(-3+8)=\left((2)/(3)\right)^(2a-1)`

If
`a^m=a^n` then
`m=n`

`-3+8=2a-1\\2a=5+1\\a=(6)/(2)\\a=3`

b)

`$(6^(4) * 9^(-2) * 25)/(2^(4) * 5^(2) * 3^(3))$=$((2*3)^(4) * 9^(-2) * 5^2)/(2^(4) * 5^(2) * 3^(3))$\\=( 2^4* 3^4* 9^(-2) )/(2^(4) * 3^(3))\\=( 3^4* 9^(-2) )/(3^(3))`

Use the property of exponent,
`(a^m)/(a^n)=a^(m-n)`

`=3^(4-3)* 9^(-2)\\=3* 9^(-2)`

Use the property of exponent,
`a^(-n)=(1)/(a^n)`

`=3* (1)/(9^2)\\=3* (1)/(81)\\= (1)/(27)`