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

Identify Base and Exponent: Identify the base and the exponent. In the expression (-(3)/(4))^(3), -(3/4) is the base raised to the exponent 3. Base: -(3/4) Exponent: 3Choose Expanded Form: Choose the expanded form of (-(3)/(4))^(3). The base is -(3/4) and the exponent is 3. So, (-(3)/(4))^(3) means -(3/4) is multiplied by itself 3 times. Expanded Form of (-(3)/(4))^(3): (-(3/4)) × (-(3/4)) × (-(3/4))Multiply to Simplify: (-(3)/(4))^(3) = (-(3/4)) × (-(3/4)) × (-(3/4)) Multiply to write in simplest form. (-(3)/(4))^(3) = (-(3/4)) × (-(3/4)) × (-(3/4)) = (9/16) × (-(3/4)) // Multiplying the first two factors = -27/64 // Multiplying the result by the third factor The simplest form of (-(3)/(4))^(3) is -27/64.

Home

Math Problems

Grade 8

Powers with negative bases

Full solution

Q. Evaluate.

\newline

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

Identify Base and Exponent: Identify the base and the exponent. $\newline$ In the expression $\left(-\frac{3}{4}\right)^{3}$ , $-\frac{3}{4}$ is the base raised to the exponent $3$ . $\newline$ Base: $-\frac{3}{4}$ $\newline$ Exponent: $3$
Choose Expanded Form: Choose the expanded form of $(-(3)/(4))^{3}$ . $\newline$ The base is $-(3/4)$ and the exponent is $3$ . $\newline$ So, $(-(3)/(4))^{3}$ means $-(3/4)$ is multiplied by itself $3$ times. $\newline$ Expanded Form of $(-(3)/(4))^{3}$ : $\newline$ $(-(3/4)) \times (-(3/4)) \times (-(3/4))$
Multiply to Simplify: $(-\frac{3}{4})^{3} = (-\frac{3}{4}) \times (-\frac{3}{4}) \times (-\frac{3}{4})$ $\newline$ Multiply to write in simplest form. $\newline$ $(-\frac{3}{4})^{3}$ $\newline$ $= (-\frac{3}{4}) \times (-\frac{3}{4}) \times (-\frac{3}{4})$ $\newline$ = \frac{$9$}{$16$} \times (-\frac{$3$}{$4$}) // Multiplying the first two factors$\newline= -\frac{\(27$}{$64$} // Multiplying the result by the third factor\(\newlineThe simplest form of $(-\frac{3}{4})^{3}$ is $-\frac{27}{64}$ .