this module is intended to help you understand fractional exponents. rewrite the expression below as 5 to a…

this module is intended to help you understand fractional exponents. rewrite the expression below as 5 to a single power: \n$(5^9)^{10}=5^{90}$\n\n$(5^3)^8=5^{24}$\n\nnow try:\n$(5^{\\frac{1}{9}})^9=\\square$

this module is intended to help you understand fractional exponents. rewrite the expression below as 5 to a single power: \n$(5^9)^{10}=5^{90}$\n\n$(5^3)^8=5^{24}$\n\nnow try:\n$(5^{\\frac{1}{9}})^9=\\square$

Answer

Explanation:

Step1: Recall exponent rule

When raising a power to a power, we multiply the exponents: ((a^m)^n = a^{m\times n}).

Step2: Apply the rule

For (\left(5^{\frac{1}{9}}\right)^9), we multiply the exponents (\frac{1}{9}) and (9): (\frac{1}{9}\times9 = 1). So the expression becomes (5^1).

Step3: Simplify (5^1)

Any number to the power of (1) is itself, so (5^1 = 5).

Answer:

(5)