Solve [(-7/4)^2]^3*[(16/35)^3]^2

$$[ ( \frac { - 7 } { 4 } ) ^ { 2 } ] ^ { 3 } \times [ ( \frac { 16 } { 35 } ) ^ { 3 } ] ^ { 2 }$$

Evaluate

$$\frac{4096}{15625}=0.262144$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.

$$\left(\frac{-7}{4}\right)^{6}\times \left(\left(\frac{16}{35}\right)^{3}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

$$\left(\frac{-7}{4}\right)^{6}\times \left(\frac{16}{35}\right)^{6}$$

Fraction \frac{-7}{4} can be rewritten as -\frac{7}{4} by extracting the negative sign.

$$\left(-\frac{7}{4}\right)^{6}\times \left(\frac{16}{35}\right)^{6}$$

Calculate -\frac{7}{4} to the power of 6 and get \frac{117649}{4096}.

$$\frac{117649}{4096}\times \left(\frac{16}{35}\right)^{6}$$

Calculate \frac{16}{35} to the power of 6 and get \frac{16777216}{1838265625}.

$$\frac{117649}{4096}\times \frac{16777216}{1838265625}$$

Multiply \frac{117649}{4096} and \frac{16777216}{1838265625} to get \frac{4096}{15625}.

$$\frac{4096}{15625}$$

Factor

$$\frac{2 ^ {12}}{5 ^ {6}} = 0.262144$$