Answer:
What you're solving forWrite an expression that is equivalent to \(x^{\frac{1}{4}}\cdot x^{\frac{2}{3}}\) in radical form.Helpful informationThe product property of exponents states that for any nonzero real numbers \(x\) and \(y\) and any rational numbers \(a\) and \(b\), \(\left(xy\right)^{a}=x^{a}\cdot y^{a}\)The power of a power property of exponents states that for any nonzero real number \(a\) and integers \(x\) and \(y\), \(\left(a^{x}\right)^{y}=a^{x\cdot y}\)The radical property of exponents states that for any nonzero real number \(a\) and integers \(x\) and \(y\), \(a^{\frac{x}{y}}=\sqrt[y]{a^{x}}\)
Step-by-step explanation:
Step 1Simplify the expression.Use the product property of exponents.\(x^{\frac{1}{4}+\frac{2}{3}}\)Add the fractions.\(x^{\frac{11}{12}}\)Step 2Rewrite the expression in radical form.Use the radical property of exponents.\(\sqrt[12]{x^{11}}\)SolutionThe required expression is \(\sqrt[12]{x^{11}}\)...... hope it will help you ｡◕‿◕｡
Answer:
Step-by-step explanation:
x^(1/4) * x ^(2/3) = x ^(1/4 + 2/3) = x^(11/12) = 12th root of x^11
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