Rewrite the expression in the form z^(n). (z^(-(1)/(3)))/(z^(-(5)/(6)))=◻

Use Exponent Property: We have the expression (z^(-(1)/(3)))/(z^(-(5)/(6))). To simplify, we use the property of exponents that says when we divide like bases, we subtract the exponents: a^m / a^n = a^(m-n).Subtract Exponents: So, (z^(-(1)/(3)))/(z^(-(5)/(6))) = z^((-(1)/(3)) - (-(5)/(6))).Find Common Denominator: Now, we need to subtract the exponents: (-(1)/(3)) - (-(5)/(6)) = (-(1)/(3)) + (5)/(6).Convert Fractions: To add these fractions, we need a common denominator. The common denominator for 3 and 6 is 6.Add Fractions: We convert (-(1)/(3)) to (-2)/(6) so that we can add it to (5)/(6).Simplify Result: Now, we add the fractions: (-2)/(6) + (5)/(6) = (3)/(6).Correct Mistake: We can simplify (3)/(6) to (1)/(2) because 3 and 6 are both divisible by 3.So, the expression becomes z^((1)/(2)).But wait, there's a mistake in the previous steps. We need to check our fraction addition again.

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Rewrite the expression in the form
z^(n).

(z^(-(1)/(3)))/(z^(-(5)/(6)))=◻

Rewrite the expression in the form $z^{n}$ . $\newline$ $\frac{z^{-\frac{1}{3}}}{z^{-\frac{5}{6}}}=\square$

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Math Problems

Algebra 2

Evaluate exponential functions

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Q. Rewrite the expression in the form

z^{n}

\newline

\frac{z^{-\frac{1}{3}}}{z^{-\frac{5}{6}}}=\square

Use Exponent Property: We have the expression $(z^{-\frac{1}{3}})/(z^{-\frac{5}{6}})$ . To simplify, we use the property of exponents that says when we divide like bases, we subtract the exponents: $a^m / a^n = a^{m-n}$ .
Subtract Exponents: So, $\frac{z^{-(1)/(3)}}{z^{-(5)/(6)}} = z^{\left(-(1)/(3)\right) - \left(-(5)/(6)\right)}$ .
Find Common Denominator: Now, we need to subtract the exponents: $\left(-\frac{1}{3}\right) - \left(-\frac{5}{6}\right) = \left(-\frac{1}{3}\right) + \frac{5}{6}.$
Convert Fractions: To add these fractions, we need a common denominator. The common denominator for $3$ and $6$ is $6$ .
Add Fractions: We convert $\left(-\frac{1}{3}\right)$ to $\left(-\frac{2}{6}\right)$ so that we can add it to $\frac{5}{6}$ .
Simplify Result: Now, we add the fractions: $\frac{-2}{6} + \frac{5}{6} = \frac{3}{6}.$
Correct Mistake: We can simplify $(3)/(6)$ to $(1)/(2)$ because $3$ and $6$ are both divisible by $3$ .
Correct Mistake: We can simplify $(3)/(6)$ to $(1)/(2)$ because $3$ and $6$ are both divisible by $3$ .So, the expression becomes $z^{(1)/(2)}$ .
Correct Mistake: We can simplify $(3)/(6)$ to $(1)/(2)$ because $3$ and $6$ are both divisible by $3$ .So, the expression becomes $z^{(1)/(2)}$ .But wait, there's a mistake in the previous steps. We need to check our fraction addition again.