Solve 45*0.03^2*0.97^2*0.97^2*0.97^2*{0.97}^2

$$45 \times { 0.03 }^{ 2 } \times { 0.97 }^{ 2 } \times { 0.97 }^{ 2 } \times { 0.97 }^{ 2 } \times { 0.97 }^{ 2 }$$

Evaluate

$$0.03174160605722669205$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.

$$45\times 0.03^{2}\times 0.97^{4}\times 0.97^{2}\times 0.97^{2}$$

To multiply powers of the same base, add their exponents. Add 4 and 2 to get 6.

$$45\times 0.03^{2}\times 0.97^{6}\times 0.97^{2}$$

To multiply powers of the same base, add their exponents. Add 6 and 2 to get 8.

$$45\times 0.03^{2}\times 0.97^{8}$$

Calculate 0.03 to the power of 2 and get 0.0009.

$$45\times 0.0009\times 0.97^{8}$$

Multiply 45 and 0.0009 to get 0.0405.

$$0.0405\times 0.97^{8}$$

Calculate 0.97 to the power of 8 and get 0.7837433594376961.

$$0.0405\times 0.7837433594376961$$

Multiply 0.0405 and 0.7837433594376961 to get 0.03174160605722669205.

$$0.03174160605722669205$$

Factor

$$\frac{3 ^ {4} \cdot 97 ^ {8}}{2 ^ {20} \cdot 5 ^ {19}} = 0.031741606057226694$$