this module is intended to help you understand fractional exponents. rewrite the expression below as 6 to a…

this module is intended to help you understand fractional exponents. rewrite the expression below as 6 to a single power: \n$(6^4)^9 = 6^{36}$\n$(6^7)^3 = 6^{21}$\nnow try:\n$(6^{\\frac{1}{8}})^8 = \\square$

this module is intended to help you understand fractional exponents. rewrite the expression below as 6 to a single power: \n$(6^4)^9 = 6^{36}$\n$(6^7)^3 = 6^{21}$\nnow try:\n$(6^{\\frac{1}{8}})^8 = \\square$

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(6^{\frac{1}{8}}\right)^8), we multiply the exponents (\frac{1}{8}) and (8): (\frac{1}{8} \times 8 = 1). So (\left(6^{\frac{1}{8}}\right)^8 = 6^1).

Step3: Simplify (6^1)

Any number to the power of (1) is itself, so (6^1 = 6).

Answer:

(6)