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

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

Evaluate

$$\frac{1}{117649}\approx 0.0000085$$

Solution Steps

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

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

Rewrite 7^{2} as 7^{-1}\times 7^{3}. Cancel out 7^{-1} in both numerator and denominator.

$$\left(\frac{1}{7^{3}}\right)^{2}$$

Calculate 7 to the power of 3 and get 343.

$$\left(\frac{1}{343}\right)^{2}$$

Calculate \frac{1}{343} to the power of 2 and get \frac{1}{117649}.

$$\frac{1}{117649}$$

Factor

$$\frac{1}{7 ^ {6}} = 8.499859752314087 \times 10^{-6}$$