Find the value of the expression: [tex]$\frac{7^2}{2^7}$[/tex]
Answer (2)
Calculate 7 2 = 49 .
Calculate 2 7 = 128 .
Divide the results: 128 49 .
The value of the expression is 128 49 .
Explanation
Understanding the Problem We are asked to find the value of the expression 2 7 7 2 . This involves calculating the square of 7 and the 7th power of 2, and then dividing the results.
Calculating the Numerator First, we calculate 7 2 , which means 7 × 7 . The result is 49.
Calculating the Denominator Next, we calculate 2 7 , which means 2 × 2 × 2 × 2 × 2 × 2 × 2 . The result is 128.
Dividing the Results Now, we divide the result of 7 2 by the result of 2 7 , which is 128 49 . To find the decimal value, we perform the division 49 ÷ 128 , which equals 0.3828125.
Final Answer Therefore, the value of the expression 2 7 7 2 is 128 49 or 0.3828125.
Examples
Understanding exponents and fractions is crucial in many real-world scenarios. For example, calculating compound interest involves raising a number to a power. If you invest money in a bank account that offers compound interest, the formula to calculate the future value of your investment includes exponents. Similarly, in physics, many formulas involve exponents, such as the formula for kinetic energy, which is 2 1 m v 2 , where v is the velocity squared. Fractions are used in everyday life, from cooking to measuring ingredients.
The value of the expression 2 7 7 2 is 128 49 , or approximately 0.3828125.
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