pre-calculus - Simplify the following as much as possible: 25 x 5^(2/3)

Simplify the following as much as possible: 25 x 5^(2/3)

5 viewed last edited 5 years ago

Anonymous

I first simplified 5^(2/3) to the cube root of 25. I left the first 25 alone because I cannot simplify it any further so my answer to this is 25 x the cube root of 25.

The answer is actually 5^ (8/3). I have no idea where the 8 came from, and how you get rid of the first 25. I need help with this please.

Mahesh Godavarti (last edited 5 years ago) (Expert, Founder @Qalaxia)

Your answer is also correct. [math] 25 = 25 \times 5^{2/3} = 25 \times \sqrt[3]{25} [/math]

However, we also can use x^a \times x^b = x^{a+b} .

25 = 5^2

25 \times 5^{2/3} = 5^2 \times 5^{2/3} = 5^{2 + 2/3} = 5^{\frac{6+2}{3}} = 5^{8/3} .