Solve [(3*5-7*2)^5+2^4:2]^3:9^2

$$[ ( 3 \cdot 5 - 7 \cdot 2 ) ^ { 5 } + 2 ^ { 4 } : 2 ] ^ { 3 } : 9 ^ { 2 }$$

Evaluate

$$9$$

Solution Steps

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

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

Multiply 3 and 5 to get 15.

$$\frac{\left(\left(15-7\times 2\right)^{5}+2^{3}\right)^{3}}{9^{2}}$$

Multiply 7 and 2 to get 14.

$$\frac{\left(\left(15-14\right)^{5}+2^{3}\right)^{3}}{9^{2}}$$

Subtract 14 from 15 to get 1.

$$\frac{\left(1^{5}+2^{3}\right)^{3}}{9^{2}}$$

Calculate 1 to the power of 5 and get 1.

$$\frac{\left(1+2^{3}\right)^{3}}{9^{2}}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{\left(1+8\right)^{3}}{9^{2}}$$

Add 1 and 8 to get 9.

$$\frac{9^{3}}{9^{2}}$$

Calculate 9 to the power of 3 and get 729.

$$\frac{729}{9^{2}}$$

Calculate 9 to the power of 2 and get 81.

$$\frac{729}{81}$$

Divide 729 by 81 to get 9.

$$9$$

Factor

$$3^{2}$$