Evaluate the expression (25^-3/2)^1/3

1/5

Step-by-step explanation:

To avoid ambiguity, your negative exponent -3/2 should be enclosed in brackets or parentheses, as should your exponent 1/3:

( 25^[-3/2] )^ (1/3)

This is equivalent to:

(√25)^(-3)· (1/3), or

5^(-1), or 1/5.

the solution of the equation is 2.23 ⇒ answer b

step-by-step explanation:

* lets revise the meaning of exponential function

- the form of the exponential function is y = ab^x, where a ≠ 0, b > 0 ,  

  b ≠ 1, and x is any real number

- it has a constant base b

- it has a variable exponent x

- to solve an exponential equation, take the log or ln of both sides,  

  and solve for the variable

* lets solve the problem

∵

- the base is 7 and the exponent is x

- insert ㏑ in both sides

∴

- use the rule

∴ x ㏑(7) = ㏑(77)

- to find x divide both sides by ㏑(7)

∴

* the solution of the equation is 2.23 to the nearest 2 decimal places