Solve 17^10div17^9+4^2*4^7div{left({4}^3right)}^2-{2}^8div{2}^4-62div2*2

$${ 17 }^{ 10 } \div { 17 }^{ 9 } + { 4 }^{ 2 } \times { 4 }^{ 7 } \div { \left( { 4 }^{ 3 } \right) }^{ 2 } - { 2 }^{ 8 } \div { 2 }^{ 4 } -62 \div 2 \times 2$$

Evaluate

$$3$$

Solution Steps

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

$$17^{1}+\frac{4^{2}\times 4^{7}}{\left(4^{3}\right)^{2}}-\frac{2^{8}}{2^{4}}-\frac{62}{2}\times 2$$

To multiply powers of the same base, add their exponents. Add 2 and 7 to get 9.

$$17^{1}+\frac{4^{9}}{\left(4^{3}\right)^{2}}-\frac{2^{8}}{2^{4}}-\frac{62}{2}\times 2$$

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

$$17^{1}+\frac{4^{9}}{4^{6}}-\frac{2^{8}}{2^{4}}-\frac{62}{2}\times 2$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 6 from 9 to get 3.

$$17^{1}+4^{3}-\frac{2^{8}}{2^{4}}-\frac{62}{2}\times 2$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 4 from 8 to get 4.

$$17^{1}+4^{3}-2^{4}-\frac{62}{2}\times 2$$

Calculate 17 to the power of 1 and get 17.

$$17+4^{3}-2^{4}-\frac{62}{2}\times 2$$

Calculate 4 to the power of 3 and get 64.

$$17+64-2^{4}-\frac{62}{2}\times 2$$

Add 17 and 64 to get 81.

$$81-2^{4}-\frac{62}{2}\times 2$$

Calculate 2 to the power of 4 and get 16.

$$81-16-\frac{62}{2}\times 2$$

Subtract 16 from 81 to get 65.

$$65-\frac{62}{2}\times 2$$

Divide 62 by 2 to get 31.

$$65-31\times 2$$

Multiply 31 and 2 to get 62.

$$65-62$$

Subtract 62 from 65 to get 3.

$$3$$

Factor

$$3$$