Question

Which expression is equivalent to left parenthesis 5 to the power of negative 2 end exponent right parenthesis to the power of 5 space x space 5 to the power of 4 ?

Answer 1

`(1)/(5^6)`

Explanation:

Given the expression (5⁻²)⁵ ₓ 5⁴

According to indices

(a^m)^n = a^{mn}

(5⁻²)⁵ = (5⁻¹⁰)

(5⁻²)⁵ ₓ 5⁴

= 5⁻¹⁰ ₓ 5⁴

= 5⁻¹⁰⁺⁴

= 5⁻⁶

Hence the equivalent expression is
`(1)/(5^6)`