Solve {left(7*7^-2/7^4right)}^2

$${ \left( \frac{ 7 \times { 7 }^{ -2 } }{ { 7 }^{ 4 } } \right) }^{ 2 }$$

Evaluate

$$\frac{1}{282475249}\approx 3.540133175 \cdot 10^{-9}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 1 and -2 to get -1.

$$\left(\frac{7^{-1}}{7^{4}}\right)^{2}$$

Rewrite 7^{4} as 7^{-1}\times 7^{5}. Cancel out 7^{-1} in both numerator and denominator.

$$\left(\frac{1}{7^{5}}\right)^{2}$$

Calculate 7 to the power of 5 and get 16807.

$$\left(\frac{1}{16807}\right)^{2}$$

Calculate \frac{1}{16807} to the power of 2 and get \frac{1}{282475249}.

$$\frac{1}{282475249}$$

Factor

$$\frac{1}{7 ^ {10}} = 3.540133174641435 \times 10^{-9}$$