what is another way to write the 1 in the expression $\\frac{1}{3^{4}}$? explain.
what is another way to write the 1 in the expression $\\frac{1}{3^{4}}$? explain.
Answer
Explanation:
Step1: Recall the rule of exponents
The rule (a^0 = 1) ((a\neq0)). Here, we can use this rule to rewrite the (1) in the fraction (\frac{1}{3^{4}}).
Step2: Apply the exponent rule
Since (1 = 3^{0}) (because for (a = 3), using the formula (a^{0}=1)), the expression (\frac{1}{3^{4}}) can be rewritten as (\frac{3^{0}}{3^{4}}).
Step3: Use the quotient - rule of exponents
The quotient rule of exponents is (\frac{a^{m}}{a^{n}}=a^{m - n}). For (a = 3), (m = 0) and (n = 4), we have (\frac{3^{0}}{3^{4}}=3^{0 - 4}=3^{- 4}).
Answer:
(3^{0}) (because (a^{0}=1) for (a\neq0), when (a = 3), (3^{0}=1)) or (3^{-4}) (since (\frac{3^{0}}{3^{4}}=3^{-4}) using the quotient rule of exponents (\frac{a^{m}}{a^{n}}=a^{m - n}))