Evaluate. (-(4)/(3))^(3)=

Identify base and exponent: Identify the base and the exponent. In the expression (-(4/3))^3, -(4/3) is the base raised to the exponent 3. Base: -(4/3) Exponent: 3Choose expanded form: Choose the expanded form of (-(4/3))^3. The base is -(4/3) and the exponent is 3. So, (-(4/3))^3 means -(4/3) is multiplied by itself 3 times. Expanded Form of (-(4/3))^3: (-(4/3)) × (-(4/3)) × (-(4/3))Multiply to simplify: (-(4/3))^3 = (-(4/3)) × (-(4/3)) × (-(4/3)) Multiply to write in simplest form. (-(4/3))^3 = (-(4/3)) × (-(4/3)) × (-(4/3)) = (-4/3) × (-4/3) × (-4/3) = (-4 × -4 × -4) / (3 × 3 × 3) = (-64) / 27 Since the base is negative and the exponent is odd, the result will be negative.Simplify the result: Simplify the result. (-64) / 27 is already in its simplest form. So, the simplest form of (-(4/3))^3 is (-64) / 27.

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Evaluate. $\newline$ $\left(-\frac{4}{3}\right)^{3}=$

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Math Problems

Grade 8

Powers with negative bases

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Q. Evaluate.

\newline

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

Identify base and exponent: Identify the base and the exponent. $\newline$ In the expression $\left(-\frac{4}{3}\right)^3$ , $-\frac{4}{3}$ is the base raised to the exponent $3$ . $\newline$ Base: $-\frac{4}{3}$ $\newline$ Exponent: $3$
Choose expanded form: Choose the expanded form of $(-(\frac{4}{3}))^3$ . The base is $-(\frac{4}{3})$ and the exponent is $3$ . So, $(-(\frac{4}{3}))^3$ means $-(\frac{4}{3})$ is multiplied by itself $3$ times. Expanded Form of $(-(\frac{4}{3}))^3$ : $(-(\frac{4}{3})) \times (-(\frac{4}{3})) \times (-(\frac{4}{3}))$
Multiply to simplify: $(-\left(\frac{4}{3}\right))^3 = (-\left(\frac{4}{3}\right)) \times (-\left(\frac{4}{3}\right)) \times (-\left(\frac{4}{3}\right))$
Multiply to write in simplest form.
$(-\left(\frac{4}{3}\right))^3$
= $(-\left(\frac{4}{3}\right)) \times (-\left(\frac{4}{3}\right)) \times (-\left(\frac{4}{3}\right))$
= $(-\frac{4}{3}) \times (-\frac{4}{3}) \times (-\frac{4}{3})$
= $(-4 \times -4 \times -4) / (3 \times 3 \times 3)$
= $(-64) / 27$
Since the base is negative and the exponent is odd, the result will be negative.
Simplify the result: Simplify the result. $\newline$ $(-64) / 27$ is already in its simplest form. $\newline$ So, the simplest form of $(-(4/3))^3$ is $(-64) / 27$ .