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Given 
x > 0, the expression 
root(8)(x^(48)) is equivalent to

x^(6)root(8)(x)

x^(5)

x^(6)

x^(5)root(8)(x)

Given x>0 , the expression x488 \sqrt[8]{x^{48}} is equivalent to\newlinex6x8 x^{6} \sqrt[8]{x} \newlinex5 x^{5} \newlinex6 x^{6} \newlinex5x8 x^{5} \sqrt[8]{x}

Full solution

Q. Given x>0 x>0 , the expression x488 \sqrt[8]{x^{48}} is equivalent to\newlinex6x8 x^{6} \sqrt[8]{x} \newlinex5 x^{5} \newlinex6 x^{6} \newlinex5x8 x^{5} \sqrt[8]{x}
  1. Rewrite expression: We are given the expression x488\sqrt[8]{x^{48}} and we need to simplify it. The 88th root of a number is the same as raising that number to the power of 18\frac{1}{8}. So, we can rewrite the expression as (x48)18(x^{48})^{\frac{1}{8}}.
  2. Apply power rule: Now we apply the power rule for exponents, which states that a^{m})^{n} = a^{m*n}\. In this case, we have \(x^{\(48\)})^{\frac{\(1\)}{\(8\)}} = x^{\(48\) * \frac{\(1\)}{\(8\)}}\
  3. Perform multiplication: We perform the multiplication in the exponent: \(48 \times \frac{1}{8} = 6. So, the expression simplifies to x(6)x^{(6)}.

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