Rewrite the expression in the form z^(n). Write the exponent as an integer, fraction, or an exact decimal (not a mixed number). root(5)(z^(4)z^(-(3)/(2)))=◻_(◻)^("+х ")

Question

Rewrite the expression in the form  z^(n). Write the exponent as an integer, fraction, or an exact decimal (not a mixed number).  root(5)(z^(4)z^(-(3)/(2)))=◻_(◻)^("+х ")

Bytelearn · Accepted Answer

Identify expression and operation: Identify the expression and the operation to be performed. The expression is root(5)(z^(4)z^(-(3)/(2))). We need to simplify the expression inside the root and then apply the fifth root.Combine exponents of z: Combine the exponents of z using the property of exponents that states z^a * z^b = z^(a+b). z^(4) * z^(-(3)/(2)) = z^(4 - (3)/(2))Convert mixed number to improper fraction: Convert the mixed number to an improper fraction to combine the exponents easily. 4 can be written as 8/2, so the expression becomes z^(8/2 - 3/2).Subtract exponents: Subtract the exponents. z^(8/2 - 3/2) = z^(5/2)Apply fifth root: Apply the fifth root to the expression. root(5)(z^(5/2)) = (z^(5/2))^(1/5)Simplify expression using exponent property: Use the property of exponents (a^(m/n))^p = a^(m/n * p) to simplify the expression. (z^(5/2))^(1/5) = z^((5/2) * (1/5))Multiply exponents: Multiply the exponents. z^((5/2) * (1/5)) = z^(5/10)Simplify exponent: Simplify the exponent. z^(5/10) = z^(1/2)

Rewrite the expression in the form $z^{n}$ . $\newline$ Write the exponent as an integer, fraction, or an exact decimal (not a mixed number). $\newline$ $\sqrt[5]{z^{4} z^{-\frac{3}{2}}}=\square$

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Rewrite the expression in the form zn z^{n} zn.\newlineWrite the exponent as an integer, fraction, or an exact decimal (not a mixed number).\newlinez4z−325=□ \sqrt[5]{z^{4} z^{-\frac{3}{2}}}=\square 5z4z−23​​=□

Rewrite the expression in the form $z^{n}$ . $\newline$ Write the exponent as an integer, fraction, or an exact decimal (not a mixed number). $\newline$ $\sqrt[5]{z^{4} z^{-\frac{3}{2}}}=\square$