Question

Which expression is equivalent to (2^3)^-5

Answer 1

The expression (2^3)^-5 is equivalent to 1/32,768.

Step-by-step explanation:

The expression (2^3)^-5 is equivalent to 2^(3*-5). To simplify, we multiply the exponents: 3 * -5 = -15. Therefore, the expression is equal to 2^-15.

When a number is raised to a negative exponent, it is equal to 1 divided by the number raised to the positive exponent. So, 2^-15 is equal to 1/(2^15).

The final expression, 1/(2^15), can also be written as 1/32,768. This is the equivalent expression to (2^3)^-5.

Answer 2

Equivalent expression is
`(1)/(2^(15))`

Step-by-step explanation:

Given expression
`(2^3)^(-5)`

Following law of exponent are used,

`(x^a)^b=x^(ab)\:\:and\:\:x^(-a)=(1)/(x^a)`

So, consider

`(2^3)^(-5)`

`=2^(3*(-5))`

`=2^(-15)`

`=(1)/(2^(15))`

Therefore, Equivalent expression is
`(1)/(2^(15))`