Select the equivalent expression. ((z^(4))/(6^(2)))^(-3)=? Choose 1 answer: (A) (z)/(6^(-1)) (B) z^(12)*6^(6) (C) (6^(6))/(z^(12))

Understand Exponent Properties: Understand the properties of exponents. When an expression with a power is raised to another power, we multiply the exponents. Also, a negative exponent means we take the reciprocal of the base and make the exponent positive.Apply Exponent Rule: Apply the exponent rule to the given expression. ((z^(4))/(6^(2)))^(-3) means we multiply the exponents of z and 6 by -3. (z^(4 * -3))/(6^(2 * -3))Calculate New Exponents: Calculate the new exponents. z^(4 * -3) becomes z^(-12) and 6^(2 * -3) becomes 6^(-6). (z^(-12))/(6^(-6))Rewrite with Positive Exponents: Rewrite the expression with positive exponents. To make the exponents positive, we take the reciprocal of each base. (6^(6))/(z^(12))Match with Options: Match the simplified expression with the given options. The expression we have found, (6^(6))/(z^(12)), matches option (C).

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Math Problems

Grade 8

Evaluate expressions using properties of exponents

Full solution

Q. Select the equivalent expression.

\newline

\left(\frac{z^{4}}{6^{2}}\right)^{-3}=

\newline

Choose

1

answer:

\newline

(A)

\frac{z}{6^{-1}}

\newline

(B)

z^{12}\cdot 6^{6}

\newline

(C)

\frac{6^{6}}{z^{12}}

Understand Exponent Properties: Understand the properties of exponents. When an expression with a power is raised to another power, we multiply the exponents. Also, a negative exponent means we take the reciprocal of the base and make the exponent positive.
Apply Exponent Rule: Apply the exponent rule to the given expression. $\newline$ $\left(\frac{z^{4}}{6^{2}}\right)^{-3}$ means we multiply the exponents of $z$ and $6$ by $-3$ . $\newline$ $\frac{z^{4 \cdot -3}}{6^{2 \cdot -3}}$
Calculate New Exponents: Calculate the new exponents. $\newline$ $z^{4 \times -3}$ becomes $z^{-12}$ and $6^{2 \times -3}$ becomes $6^{-6}$ . $\newline$ $\frac{z^{-12}}{6^{-6}}$
Rewrite with Positive Exponents: Rewrite the expression with positive exponents. $\newline$ To make the exponents positive, we take the reciprocal of each base. $\newline$ $\frac{6^{6}}{z^{12}}$
Match with Options: Match the simplified expression with the given options. $\newline$ The expression we have found, $(6^{6})/(z^{12})$ , matches option (C).