Solve 4^{9}:4^{8}-{[4^2+3*(11^2-9^2)]-10^5}

$$4 ^ { 9 } : 4 ^ { 8 } - \{ [ 4 ^ { 2 } + 3 \times ( 11 ^ { 2 } - 9 ^ { 2 } ) ] - 10 ^ { 5 } \}$$

Evaluate

$$99868$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 8 from 9 to get 1.

$$4^{1}-\left(4^{2}+3\left(11^{2}-9^{2}\right)-10^{5}\right)$$

Calculate 4 to the power of 1 and get 4.

$$4-\left(4^{2}+3\left(11^{2}-9^{2}\right)-10^{5}\right)$$

Calculate 4 to the power of 2 and get 16.

$$4-\left(16+3\left(11^{2}-9^{2}\right)-10^{5}\right)$$

Calculate 11 to the power of 2 and get 121.

$$4-\left(16+3\left(121-9^{2}\right)-10^{5}\right)$$

Calculate 9 to the power of 2 and get 81.

$$4-\left(16+3\left(121-81\right)-10^{5}\right)$$

Subtract 81 from 121 to get 40.

$$4-\left(16+3\times 40-10^{5}\right)$$

Multiply 3 and 40 to get 120.

$$4-\left(16+120-10^{5}\right)$$

Add 16 and 120 to get 136.

$$4-\left(136-10^{5}\right)$$

Calculate 10 to the power of 5 and get 100000.

$$4-\left(136-100000\right)$$

Subtract 100000 from 136 to get -99864.

$$4-\left(-99864\right)$$

The opposite of -99864 is 99864.

$$4+99864$$

Add 4 and 99864 to get 99868.

$$99868$$

Factor

$$2^{2}\times 24967$$