Solve (4^{2})^{2}:(4^{10}:4^{9})-[(2+2^{2}*9)*3-6*3^{2}]+5^7:(2^2+1)^5-2*2^2

$$( 4 ^ { 2 } ) ^ { 2 } : ( 4 ^ { 10 } : 4 ^ { 9 } ) - [ ( 2 + 2 ^ { 2 } \times 9 ) \times 3 - 6 \times 3 ^ { 2 } ] + 5 ^ { 7 } : ( 2 ^ { 2 } + 1 ) ^ { 5 } - 2 \times 2 ^ { 2 }$$

Evaluate

$$21$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$\frac{4^{4}}{\frac{4^{10}}{4^{9}}}-\left(\left(2+2^{2}\times 9\right)\times 3-6\times 3^{2}\right)+\frac{5^{7}}{\left(2^{2}+1\right)^{5}}-2\times 2^{2}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 9 from 10 to get 1.

$$\frac{4^{4}}{4^{1}}-\left(\left(2+2^{2}\times 9\right)\times 3-6\times 3^{2}\right)+\frac{5^{7}}{\left(2^{2}+1\right)^{5}}-2\times 2^{2}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 1 from 4 to get 3.

$$4^{3}-\left(\left(2+2^{2}\times 9\right)\times 3-6\times 3^{2}\right)+\frac{5^{7}}{\left(2^{2}+1\right)^{5}}-2\times 2^{2}$$

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$4^{3}-\left(\left(2+2^{2}\times 9\right)\times 3-6\times 3^{2}\right)+\frac{5^{7}}{\left(2^{2}+1\right)^{5}}-2^{3}$$

Calculate 4 to the power of 3 and get 64.

$$64-\left(\left(2+2^{2}\times 9\right)\times 3-6\times 3^{2}\right)+\frac{5^{7}}{\left(2^{2}+1\right)^{5}}-2^{3}$$

Calculate 2 to the power of 2 and get 4.

$$64-\left(\left(2+4\times 9\right)\times 3-6\times 3^{2}\right)+\frac{5^{7}}{\left(2^{2}+1\right)^{5}}-2^{3}$$

Multiply 4 and 9 to get 36.

$$64-\left(\left(2+36\right)\times 3-6\times 3^{2}\right)+\frac{5^{7}}{\left(2^{2}+1\right)^{5}}-2^{3}$$

Add 2 and 36 to get 38.

$$64-\left(38\times 3-6\times 3^{2}\right)+\frac{5^{7}}{\left(2^{2}+1\right)^{5}}-2^{3}$$

Multiply 38 and 3 to get 114.

$$64-\left(114-6\times 3^{2}\right)+\frac{5^{7}}{\left(2^{2}+1\right)^{5}}-2^{3}$$

Calculate 3 to the power of 2 and get 9.

$$64-\left(114-6\times 9\right)+\frac{5^{7}}{\left(2^{2}+1\right)^{5}}-2^{3}$$

Multiply 6 and 9 to get 54.

$$64-\left(114-54\right)+\frac{5^{7}}{\left(2^{2}+1\right)^{5}}-2^{3}$$

Subtract 54 from 114 to get 60.

$$64-60+\frac{5^{7}}{\left(2^{2}+1\right)^{5}}-2^{3}$$

Subtract 60 from 64 to get 4.

$$4+\frac{5^{7}}{\left(2^{2}+1\right)^{5}}-2^{3}$$

Calculate 5 to the power of 7 and get 78125.

$$4+\frac{78125}{\left(2^{2}+1\right)^{5}}-2^{3}$$

Calculate 2 to the power of 2 and get 4.

$$4+\frac{78125}{\left(4+1\right)^{5}}-2^{3}$$

Add 4 and 1 to get 5.

$$4+\frac{78125}{5^{5}}-2^{3}$$

Calculate 5 to the power of 5 and get 3125.

$$4+\frac{78125}{3125}-2^{3}$$

Divide 78125 by 3125 to get 25.

$$4+25-2^{3}$$

Add 4 and 25 to get 29.

$$29-2^{3}$$

Calculate 2 to the power of 3 and get 8.

$$29-8$$

Subtract 8 from 29 to get 21.

$$21$$

Factor

$$3\times 7$$