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Can you please simplify these expressions in two forms: radical and simplified without exponents?

I don't really understand how fractional exponents work, so an explanation would be appreciated.
27^4/3
36^3/2
(1/8)^2/3
128^5/7
Thank you :)

User Khelwood
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7.8k points

1 Answer

4 votes

Answer:

(a.) 27^4/3 = 81, (b.) 36^3/2 = 216, (c.) (1/8)^2/3 = 1/4, (d.) 128^5/7 = 32

Explanation:

All these expressions can be converted in square roots.

In order to do this, we can picture the fractional exponents as exponent / index

(a.) So for this first problem, we would have the cube root of
27^{(4)/(3) } or


\sqrt[3]{(27)^(4) }.

We must do the equation inside the radical first (i.e.,
(27)^(4)) to get
\sqrt[3]{531,441} = 81

We can follow these same steps for the remaining equations:

(b.)
36^{(3)/(2) } =
√((36)^3) =
√(46,656) = 216

(c.)
((1)/(8))^(2)/(3) =
\sqrt[3]{((1)/(8))^(2) } =
\sqrt[3]{((1^2)/(8^2)) } =
\sqrt[3]{((1)/(64)) } =
(1)/(4)

(d.)
128^{(5)/(7) } =
\sqrt[7]{(128)^(5) } = 32

User Lela
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