Solve निम्नलिखित परिमेय संख्या के रूप में व्यक्त करें। ( i) (4/5) ^ 3 ( ii) (- 3/7) ^ 3 (iii) (- 1/3) ^ 4 (iv) (- 5/- 11) ^ 3 | Equatix - Math Solver

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Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

$$( \frac { 4 } { 5 } ) ^ { 3 } \quad ( \frac { - 3 } { 7 } ) ^ { 3 } \quad ( \frac { - 1 } { 3 } ) ^ { 4 } \quad ( \frac { - 5 } { - 11 } ) ^ { 3 }$$

Evaluate

$-\frac{64}{1369599}\approx -0.000046729$

Solution Steps

Calculate $\frac{4}{5}$ to the power of $3$ and get $\frac{64}{125}$.

$$\frac{64}{125}\times \left(\frac{-3}{7}\right)^{3}\times \left(\frac{-1}{3}\right)^{4}\times \left(\frac{-5}{-11}\right)^{3}$$

Fraction $\frac{-3}{7}$ can be rewritten as $-\frac{3}{7}$ by extracting the negative sign.

$$\frac{64}{125}\left(-\frac{3}{7}\right)^{3}\times \left(\frac{-1}{3}\right)^{4}\times \left(\frac{-5}{-11}\right)^{3}$$

Calculate $-\frac{3}{7}$ to the power of $3$ and get $-\frac{27}{343}$.

$$\frac{64}{125}\left(-\frac{27}{343}\right)\times \left(\frac{-1}{3}\right)^{4}\times \left(\frac{-5}{-11}\right)^{3}$$

Multiply $\frac{64}{125}$ and $-\frac{27}{343}$ to get $-\frac{1728}{42875}$.

$$-\frac{1728}{42875}\times \left(\frac{-1}{3}\right)^{4}\times \left(\frac{-5}{-11}\right)^{3}$$

Fraction $\frac{-1}{3}$ can be rewritten as $-\frac{1}{3}$ by extracting the negative sign.

$$-\frac{1728}{42875}\left(-\frac{1}{3}\right)^{4}\times \left(\frac{-5}{-11}\right)^{3}$$

Calculate $-\frac{1}{3}$ to the power of $4$ and get $\frac{1}{81}$.

$$-\frac{1728}{42875}\times \frac{1}{81}\times \left(\frac{-5}{-11}\right)^{3}$$

Multiply $-\frac{1728}{42875}$ and $\frac{1}{81}$ to get $-\frac{64}{128625}$.

$$-\frac{64}{128625}\times \left(\frac{-5}{-11}\right)^{3}$$

Fraction $\frac{-5}{-11}$ can be simplified to $\frac{5}{11}$ by removing the negative sign from both the numerator and the denominator.

$$-\frac{64}{128625}\times \left(\frac{5}{11}\right)^{3}$$

Calculate $\frac{5}{11}$ to the power of $3$ and get $\frac{125}{1331}$.

$$-\frac{64}{128625}\times \frac{125}{1331}$$

Multiply $-\frac{64}{128625}$ and $\frac{125}{1331}$ to get $-\frac{64}{1369599}$.

$$-\frac{64}{1369599}$$

Factor

$-\frac{64}{1369599} = -4.6729006081342055 \times 10^{-5}$