Solve 7*2^{3}-24^{3}:8^{3}-5^{2}+2*2^2-18:3^2-3^5:3^3

$$7 \times 2 ^ { 3 } - 24 ^ { 3 } : 8 ^ { 3 } - 5 ^ { 2 } + 2 \times 2 ^ { 2 } - 18 : 3 ^ { 2 } - 3 ^ { 5 } : 3 ^ { 3 }$$

Evaluate

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Solution Steps

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

$$7\times 2^{3}-\frac{24^{3}}{8^{3}}-5^{2}+2^{3}-\frac{18}{3^{2}}-\frac{3^{5}}{3^{3}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 3 from 5 to get 2.

$$7\times 2^{3}-\frac{24^{3}}{8^{3}}-5^{2}+2^{3}-\frac{18}{3^{2}}-3^{2}$$

Calculate 2 to the power of 3 and get 8.

$$7\times 8-\frac{24^{3}}{8^{3}}-5^{2}+2^{3}-\frac{18}{3^{2}}-3^{2}$$

Multiply 7 and 8 to get 56.

$$56-\frac{24^{3}}{8^{3}}-5^{2}+2^{3}-\frac{18}{3^{2}}-3^{2}$$

Calculate 24 to the power of 3 and get 13824.

$$56-\frac{13824}{8^{3}}-5^{2}+2^{3}-\frac{18}{3^{2}}-3^{2}$$

Calculate 8 to the power of 3 and get 512.

$$56-\frac{13824}{512}-5^{2}+2^{3}-\frac{18}{3^{2}}-3^{2}$$

Divide 13824 by 512 to get 27.

$$56-27-5^{2}+2^{3}-\frac{18}{3^{2}}-3^{2}$$

Subtract 27 from 56 to get 29.

$$29-5^{2}+2^{3}-\frac{18}{3^{2}}-3^{2}$$

Calculate 5 to the power of 2 and get 25.

$$29-25+2^{3}-\frac{18}{3^{2}}-3^{2}$$

Subtract 25 from 29 to get 4.

$$4+2^{3}-\frac{18}{3^{2}}-3^{2}$$

Calculate 2 to the power of 3 and get 8.

$$4+8-\frac{18}{3^{2}}-3^{2}$$

Add 4 and 8 to get 12.

$$12-\frac{18}{3^{2}}-3^{2}$$

Calculate 3 to the power of 2 and get 9.

$$12-\frac{18}{9}-3^{2}$$

Divide 18 by 9 to get 2.

$$12-2-3^{2}$$

Subtract 2 from 12 to get 10.

$$10-3^{2}$$

Calculate 3 to the power of 2 and get 9.

$$10-9$$

Subtract 9 from 10 to get 1.

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Factor

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