Solve [(3^{8}*3^{4}*3):3^{10}]:9+[(4^{7}*4*4^{3}*4^2)^2:2^26:2^24]

$$[ ( 3 ^ { 8 } \times 3 ^ { 4 } \times 3 ) : 3 ^ { 10 } ] : 9 + [ ( 4 ^ { 7 } \times 4 \times 4 ^ { 3 } \times 4 ^ { 2 } ) ^ { 2 } : 2 ^ { 26 } : 2 ^ { 24 } ]$$

Evaluate

$$7$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 8 and 4 to get 12.

$$\frac{\frac{3^{12}\times 3}{3^{10}}}{9}+\frac{\frac{\left(4^{7}\times 4\times 4^{3}\times 4^{2}\right)^{2}}{2^{26}}}{2^{24}}$$

To multiply powers of the same base, add their exponents. Add 12 and 1 to get 13.

$$\frac{\frac{3^{13}}{3^{10}}}{9}+\frac{\frac{\left(4^{7}\times 4\times 4^{3}\times 4^{2}\right)^{2}}{2^{26}}}{2^{24}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 10 from 13 to get 3.

$$\frac{3^{3}}{9}+\frac{\frac{\left(4^{7}\times 4\times 4^{3}\times 4^{2}\right)^{2}}{2^{26}}}{2^{24}}$$

To multiply powers of the same base, add their exponents. Add 7 and 1 to get 8.

$$\frac{3^{3}}{9}+\frac{\frac{\left(4^{8}\times 4^{3}\times 4^{2}\right)^{2}}{2^{26}}}{2^{24}}$$

To multiply powers of the same base, add their exponents. Add 8 and 3 to get 11.

$$\frac{3^{3}}{9}+\frac{\frac{\left(4^{11}\times 4^{2}\right)^{2}}{2^{26}}}{2^{24}}$$

To multiply powers of the same base, add their exponents. Add 11 and 2 to get 13.

$$\frac{3^{3}}{9}+\frac{\frac{\left(4^{13}\right)^{2}}{2^{26}}}{2^{24}}$$

To raise a power to another power, multiply the exponents. Multiply 13 and 2 to get 26.

$$\frac{3^{3}}{9}+\frac{\frac{4^{26}}{2^{26}}}{2^{24}}$$

Calculate 3 to the power of 3 and get 27.

$$\frac{27}{9}+\frac{\frac{4^{26}}{2^{26}}}{2^{24}}$$

Divide 27 by 9 to get 3.

$$3+\frac{\frac{4^{26}}{2^{26}}}{2^{24}}$$

Calculate 4 to the power of 26 and get 4503599627370496.

$$3+\frac{\frac{4503599627370496}{2^{26}}}{2^{24}}$$

Calculate 2 to the power of 26 and get 67108864.

$$3+\frac{\frac{4503599627370496}{67108864}}{2^{24}}$$

Divide 4503599627370496 by 67108864 to get 67108864.

$$3+\frac{67108864}{2^{24}}$$

Calculate 2 to the power of 24 and get 16777216.

$$3+\frac{67108864}{16777216}$$

Divide 67108864 by 16777216 to get 4.

$$3+4$$

Add 3 and 4 to get 7.

$$7$$

Factor

$$7$$