Simplify. Rewrite the expression in the form z^(n). (z^(7))/(z^(-14))=

Identify base and exponents: Identify the base and the exponents of both the numerator and the denominator. In the numerator, z is the base raised to the exponent 7. In the denominator, z is the base raised to the exponent -14. Base: z Exponent of numerator: 7 Exponent of denominator: -14Apply quotient rule for exponents: Apply the quotient rule for exponents, which states that when dividing like bases, you subtract the exponent of the denominator from the exponent of the numerator. (z^(7))/(z^(-14)) = z^(7 - (-14))Perform subtraction in exponent: Perform the subtraction in the exponent. z^(7 - (-14)) = z^(7 + 14) = z^(21)Write final simplified expression: Write the final simplified expression. The expression (z^(7))/(z^(-14)) simplifies to z^(21).

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

(z^(7))/(z^(-14))=

Simplify. $\newline$ Rewrite the expression in the form $\newline$ $z^{n}$ . $\newline$ $\frac{z^{7}}{z^{-14}}$ =

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Math Problems

Grade 8

Evaluate expressions using properties of exponents

Full solution

Q. Simplify.

\newline

Rewrite the expression in the form

\newline

z^{n}

\newline

\frac{z^{7}}{z^{-14}}

Identify base and exponents: Identify the base and the exponents of both the numerator and the denominator. In the numerator, $z$ is the base raised to the exponent $7$ . In the denominator, $z$ is the base raised to the exponent $-14$ .
Base: $z$
Exponent of numerator: $7$
Exponent of denominator: $-14$
Apply quotient rule for exponents: Apply the quotient rule for exponents, which states that when dividing like bases, you subtract the exponent of the denominator from the exponent of the numerator. $\newline$ $\frac{z^{7}}{z^{-14}} = z^{7 - (-14)}$
Perform subtraction in exponent: Perform the subtraction in the exponent. $\newline$ $z^{(7 - (-14))} = z^{(7 + 14)} = z^{21}$
Write final simplified expression: Write the final simplified expression. $\newline$ The expression $\frac{z^{7}}{z^{-14}}$ simplifies to $z^{21}$ .