Question

this module is intended to help you understand fractional exponents. rewrite the expression below as 9 to a single power:
$(9^5)^7 = 9^{35}$
$(9^8)^4 = 9^{32}$
now try:
$(9^{\frac{1}{9}})^9 = \square$

Explanation:

Step1: Recall exponent rule

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

Step2: Apply the rule

For the expression \((9^{\frac{1}{9}})^9\), we multiply the exponents \(\frac{1}{9}\) and \(9\). So we calculate \(\frac{1}{9} \times 9\).
\(\frac{1}{9} \times 9 = 1\)
So \((9^{\frac{1}{9}})^9 = 9^1\)

Step3: Simplify \(9^1\)

Any number to the power of 1 is the number itself, so \(9^1 = 9\).

Answer:

\(9\)