31 (65times 10^2)times (39times 10^3)=underline ( ) 32 (7times 2^5)-4(4times 5^5)=underline ( ) 33 77times 10^-2=underline ( ) 34 6^6times 2(3-7^-2)=underline ( ) 35 (35times 10^-2)-(57times 10^-3)=underline ( ) 36 (45times 10^3)-(63times 10^-3)=underline ( ) 37 4(23+17)^2+4(14-3)^3+50-44=underline ( ) 38 15(2^2-10)+(3^-3+9)-18+2=underline ( )

## Step1: Calculate $65 \times 10^2 \times 39 \times 10^3$<br />### Multiply the coefficients and add the exponents of 10: $(65 \times 39) \times 10^{2+3} = 2535 \times 10^5 = 2.535 \times 10^8$<br /><br />## Step2: Calculate $7 \times 2^5 - 4(4 \times 5^5)$<br />### Evaluate the exponents and then perform the multiplications and subtraction: $7 \times 32 - 4(4 \times 3125) = 224 - 4(12500) = 224 - 50000 = -49776$<br /><br />## Step3: Calculate $77 \times 10^{-2}$<br />### Move the decimal point two places to the left: $0.77$<br /><br />## Step4: Calculate $6^6 \times 2(3 - 7^{-2})$<br />### Evaluate the exponent and then perform the operations inside the parentheses, followed by multiplication: $46656 \times 2(3 - \frac{1}{49}) = 46656 \times 2(\frac{147-1}{49}) = 46656 \times 2(\frac{146}{49}) = 93312 \times \frac{146}{49} = \frac{13618912}{49} \approx 277937$<br /><br />## Step5: Calculate $(35 \times 10^{-2}) - (57 \times 10^{-3})$<br />### Convert to decimal form and subtract: $0.35 - 0.057 = 0.293$<br /><br />## Step6: Calculate $(45 \times 10^3) - (63 \times 10^{-3})$<br />### Convert to decimal form and subtract: $45000 - 0.063 = 44999.937$<br /><br />## Step7: Calculate $4(23+17)^2 + 4(14-3)^3 + 50 - 44$<br />### Perform the operations inside the parentheses first, then exponents, multiplication, and finally addition/subtraction: $4(40)^2 + 4(11)^3 + 50 - 44 = 4(1600) + 4(1331) + 6 = 6400 + 5324 + 6 = 11730$<br /><br />## Step8: Calculate $15(2^2 - 10) + (3^{-3} + 9) - 18 + 2$<br />### Evaluate the exponents and then perform the operations inside the parentheses, followed by multiplication and addition/subtraction: $15(4 - 10) + (\frac{1}{27} + 9) - 18 + 2 = 15(-6) + (\frac{244}{27}) - 16 = -90 + \frac{244}{27} - 16 = -106 + \frac{244}{27} = \frac{-2862 + 244}{27} = \frac{-2618}{27} \approx -96.96$