Question

the sides of a square are five to the power of two fifths inches long. what is the area of the square? five to the power of four fifths square inches five to the power of four twenty fifths square inches twenty five to the power of four fifths square inches twenty five to the power of four twenty fifths square inches

Answer 1

The area of a square is given by;
Area=$side^{2}$
Area=$5^{ \frac{2}{5} } * 5^{ \frac{2}{5} }$
Basing on the law of indices;
$a^{m} + a^{n}$=$a^{m+n}$
so,
$5^{ \frac{2}{5} } * 5^{ \frac{2}{5} } = 5^{ \frac{2}{5}+ \frac{2}{5} } = 5^{ \frac{4}{5} } square inches$

Answer 2

Answer:

$5^{\frac{4}{5}}$

Step-by-step explanation:

We know that the area of a square is given by the formula

Area =$s^2$

Where s is the side of the square which is $5^{\frac{2}{5}}$ in our problem.

Hence the area can be calculated as

Area=$(5^{\frac{2}{5}})^{2}$

Here we apply the exponent rule which says

$(x^{a})^{b}=x^{ab}$

Hence

$(5^{\frac{2}{5}})^{2}=5^{\frac{2*2}{5}}$

$(5^{\frac{2}{5}})^{2}=5^{\frac{4}{5}}$

Answer : $Area= 5^{\frac{4}{5}}$