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Simplify the following expression to simplest form using only positive exponents.Answer:
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Q. Simplify the following expression to simplest form using only positive exponents.Answer:
- Understand and Apply Power Rule: Understand the expression and apply the power rule.The expression is . According to the power rule , we can distribute the exponent to each factor inside the parentheses.
- Apply Power Rule to Each Factor: Apply the power rule to each factor.(64^{1/3}) \times (x^{-24 \times (1/3)}) \times (y^{3 \times (1/3)})\(\newline= 4 \times x^{-8} \times y^{1}We know that \$64^{1/3}\) is the cube root of \(64\), which is \(4\). We multiply the exponents for \(x\) and \(y\) by \(1/3\).
- Convert Negative Exponents: Convert negative exponents to positive exponents.\(\newline\)To convert \(x^{-8}\) to a positive exponent, we write it as \(1/x^{8}\). The \(y\) term already has a positive exponent.\(\newline\)= \(4 \times (1/x^{8}) \times y\)
- Write Final Simplified Expression: Write the final simplified expression.\(\newline\)The expression is now simplified to:\(\newline\)\(\frac{4y}{x^8}\)\(\newline\)This is the simplest form using only positive exponents.
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