Solve |(2/3)^5*(7/2)^5=

$$| ( \frac { 2 } { 3 } ) ^ { 5 } \cdot ( \frac { 7 } { 2 } ) ^ { 5 } =$$

Evaluate

$$\frac{16807}{243}\approx 69.164609053$$

Solution Steps

Calculate \frac{2}{3} to the power of 5 and get \frac{32}{243}.

$$|\frac{32}{243}\times \left(\frac{7}{2}\right)^{5}|$$

Calculate \frac{7}{2} to the power of 5 and get \frac{16807}{32}.

$$|\frac{32}{243}\times \frac{16807}{32}|$$

Multiply \frac{32}{243} times \frac{16807}{32} by multiplying numerator times numerator and denominator times denominator.

$$|\frac{32\times 16807}{243\times 32}|$$

Cancel out 32 in both numerator and denominator.

$$|\frac{16807}{243}|$$

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of \frac{16807}{243} is \frac{16807}{243}.

$$\frac{16807}{243}$$

Factor

$$\frac{7 ^ {5}}{3 ^ {5}} = 69\frac{40}{243} = 69.16460905349794$$