Solve ((5x^{8})^3-(x^12)^2):31x^24

$$( ( 5 x ^ { 8 } ) ^ { 3 } - ( x ^ { 12 } ) ^ { 2 } ) : 31 x ^ { 24 }$$

Evaluate

$$4x^{48}$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 12 and 2 to get 24.

$$\frac{\left(5x^{8}\right)^{3}-x^{24}}{31}x^{24}$$

Expand \left(5x^{8}\right)^{3}.

$$\frac{5^{3}\left(x^{8}\right)^{3}-x^{24}}{31}x^{24}$$

To raise a power to another power, multiply the exponents. Multiply 8 and 3 to get 24.

$$\frac{5^{3}x^{24}-x^{24}}{31}x^{24}$$

Calculate 5 to the power of 3 and get 125.

$$\frac{125x^{24}-x^{24}}{31}x^{24}$$

Combine 125x^{24} and -x^{24} to get 124x^{24}.

$$\frac{124x^{24}}{31}x^{24}$$

Divide 124x^{24} by 31 to get 4x^{24}.

$$4x^{24}x^{24}$$

To multiply powers of the same base, add their exponents. Add 24 and 24 to get 48.

$$4x^{48}$$

Expand

$$4x^{48}$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 12 and 2 to get 24.

$$\frac{\left(5x^{8}\right)^{3}-x^{24}}{31}x^{24}$$

Expand \left(5x^{8}\right)^{3}.

$$\frac{5^{3}\left(x^{8}\right)^{3}-x^{24}}{31}x^{24}$$

To raise a power to another power, multiply the exponents. Multiply 8 and 3 to get 24.

$$\frac{5^{3}x^{24}-x^{24}}{31}x^{24}$$

Calculate 5 to the power of 3 and get 125.

$$\frac{125x^{24}-x^{24}}{31}x^{24}$$

Combine 125x^{24} and -x^{24} to get 124x^{24}.

$$\frac{124x^{24}}{31}x^{24}$$

Divide 124x^{24} by 31 to get 4x^{24}.

$$4x^{24}x^{24}$$

To multiply powers of the same base, add their exponents. Add 24 and 24 to get 48.

$$4x^{48}$$