Solve 4*{left(5/4right)}^24*5/4+1=

$$4 \times { \left( \frac{ 5 }{ 4 } \right) }^{ 2 } 4 \times \frac{ 5 }{ 4 } +1=$$

Evaluate

$$\frac{129}{4}=32.25$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$4\times \left(\frac{5}{4}\right)^{3}\times 4+1$$

Calculate \frac{5}{4} to the power of 3 and get \frac{125}{64}.

$$4\times \frac{125}{64}\times 4+1$$

Express 4\times \frac{125}{64} as a single fraction.

$$\frac{4\times 125}{64}\times 4+1$$

Multiply 4 and 125 to get 500.

$$\frac{500}{64}\times 4+1$$

Reduce the fraction \frac{500}{64} to lowest terms by extracting and canceling out 4.

$$\frac{125}{16}\times 4+1$$

Express \frac{125}{16}\times 4 as a single fraction.

$$\frac{125\times 4}{16}+1$$

Multiply 125 and 4 to get 500.

$$\frac{500}{16}+1$$

Reduce the fraction \frac{500}{16} to lowest terms by extracting and canceling out 4.

$$\frac{125}{4}+1$$

Convert 1 to fraction \frac{4}{4}.

$$\frac{125}{4}+\frac{4}{4}$$

Since \frac{125}{4} and \frac{4}{4} have the same denominator, add them by adding their numerators.

$$\frac{125+4}{4}$$

Add 125 and 4 to get 129.

$$\frac{129}{4}$$

Factor

$$\frac{3 \cdot 43}{2 ^ {2}} = 32\frac{1}{4} = 32.25$$