Evaluate [(26 + 37)/121]^(3/2)

= [(2√27)^3 + (2√36)^3] / [(2√121)^3]
= [(2√27)^3 + 6] / 1331

and now... I don't know what to do...

the answer is (189/1331)(√7)... BUT I don't know how to get this! Please help me! Thanks.

[(26 + 37)/121]^(3/2)

= [63/121]^(3/2)
= [9*7)^(3/2) / 1331
= [27*√7*√7*√7]/1331
= 27*7*√7/1331
= 189√7/1331

I get what you did up until...

= [27*√7*√7*√7]/1331

Why is it √7 three times instead of √27??? I also don't get why 27 isn't √27...

To evaluate the expression [(26 + 37)/121]^(3/2), let's break it down step by step.

Step 1: Simplify the numerator and denominator separately.
Numerator: 26 + 37 = 63
Denominator: 121

So the expression becomes (63/121)^(3/2).

Step 2: Simplify the exponent.
The exponent is 3/2.

To evaluate an exponent of a fraction, you can write it as a radical. Specifically, the expression a^(m/n) is equal to the nth root of a^m. In this case, we have (63/121)^(3/2), which means it equals the square root of (63/121)^3.

Step 3: Simplify the base expression.
To evaluate the base expression (63/121)^3, we can compute it as (63^3)/(121^3).

Numerator: 63^3 = 63 × 63 × 63 = 250,047
Denominator: 121^3 = 121 × 121 × 121 = 1,771,561

So the base expression simplifies to (250,047/1,771,561).

Step 4: Combine the simplified base and exponent expressions.
Now we can combine the base and exponent expressions [(63/121)^3]^(1/2) = √(250,047/1,771,561).

To simplify the square root expression, we can divide the numerator and denominator by their greatest common divisor (GCD), which is 7:
Numerator: 250,047 ÷ 7 = 35,721
Denominator: 1,771,561 ÷ 7 = 253,223

So, the expression becomes √(35,721/253,223).

Therefore, the final answer is (35,721/253,223)√7.

Note: The expression you provided in your question, (189/1331)√7, is not equal to the expression [(26 + 37)/121]^(3/2). It seems to be a different calculation or a mistake.