Question

Evaluate:

`(25/4)^((-1)/2) - (1/27)^(1/3) + 7^0`

Answer 1

Let’s evaluate:

`(25/4)^(-1/2) - (1/27)^(1/3) + 7^0`

Step 1: Evaluate each part

1. `(25/4)^(-1/2)`

• `(25/4)^(1/2) = sqrt(25)/sqrt(4) = 5/2`
• Then apply negative exponent:
  `(25/4)^(-1/2) = 1/(5/2) = 2/5`

2. `(1/27)^(1/3) = 1/root(3)(27) = 1/3`

3. 7⁰ = 1

Step 2: Combine all parts

`2/5 - 1/3 + 1`

Find a common denominator for fractions:

`2/5 = 6/15`

`1/3 = 5/15`

`6/15 - 5/15 + 1`

= `1/15 + 1`

= `1 1/15`