rewrite the following without an exponent. \\(\\left(\\frac{3}{4}\\right)^{-3}\\)

Explanation:

Step1: Recall negative exponent rule

The rule for a negative exponent is ( a^{-n}=\frac{1}{a^{n}} ) (or ( \left(\frac{b}{c}\right)^{-n}=\left(\frac{c}{b}\right)^{n} ) for a fractional base). For ( \left(\frac{3}{4}\right)^{-3} ), we use the property of negative exponents: ( \left(\frac{a}{b}\right)^{-m}=\left(\frac{b}{a}\right)^{m} ). So, ( \left(\frac{3}{4}\right)^{-3}=\left(\frac{4}{3}\right)^{3} ).

Step2: Expand the positive exponent

Now, expand ( \left(\frac{4}{3}\right)^{3} ) using the rule ( \left(\frac{x}{y}\right)^{k}=\frac{x^{k}}{y^{k}} ). So, ( \left(\frac{4}{3}\right)^{3}=\frac{4^{3}}{3^{3}} ).

Step3: Calculate the powers

Calculate ( 4^{3}=4\times4\times4 = 64 ) and ( 3^{3}=3\times3\times3 = 27 ). Thus, ( \frac{4^{3}}{3^{3}}=\frac{64}{27} ).

Answer:

(\frac{64}{27})