Question

A rectangle has a length of the fifth root of 16 inches and a width of 2 to the 1 over 5 power inches. Find the area of the rectangle.

2 to the 3 over 5 power inches squared

2 to the 4 over 5 power inches squared

2 inches squared

2 to the 2 over 5 power inches squared

Answer 1

Do you still need help with this?

Answer 2

\( \large a^{\frac{1}{n}} = \sqrt[n] a\)

Answer 3

\[(5^{3/4})^{2/2}=5^{3/4*2/2}=5^{6/12}=5^{1/2}=\sqrt{5}\]

Answer 4

A = LW
1. Change the length into a power using the rule above.
2. Change 16 into a power of 2. Use the rule \((a^m)^n = a^{mn} \) to simplify the length.
3. Multiply the length and width using \(a^ma^n = a^{m + n} \).

Answer 5

@YanaSidlinskiy What is 2/2 = ?

Answer 6

Umm....1...

Answer 7

Great.
That means that \((5^{3/4})^{2/2}=(5^{3/4})^1 =5^{3/4} = \sqrt[4]{5^3} \)