Question

Rewrite the expression with a rational exponent as a radical expression.

five to the three fourths power all raised to the two thirds power

Answer 1

`√(5)`

Explanation:

we know that

The "power rule" tells us that to raise a power to a power, just multiply the exponents

so

`(a^(m))^(n)=a^(m*n)`

we have

`(5^{(3)/(4)})^{(2)/(3)}`

Applying the "power rule"

`(5^{(3)/(4)})^{(2)/(3)}=5^{(3)/(4)*(2)/(3)}=5^{(1)/(2)}=√(5)`