Numerical Values and Exponents

Unformatted Page Header Scratchpad Data

• Listed numerical values and expressions from header scratchwork:
  • $3$
  • $21800$
  • $9'0\,o$
  • $2460$
  • $3225$
  • Scratch line $3600$ with factor sequence $2 \times 2 \times 2 \times 27$
  • Numerical string $3937575$
  • Equation value $= 24378$
  • Denominator/Scratch value $3600$
  • Value $3$
  • Symbol sequence $7'S$
  • Symbols $S$, $S$
  • Value $25$
  • Symbols $S$, $S$

Numerical Value Calculations of Exponential Expressions

• Directive: Write the exact numerical value of each exponential expression provided.

• Problem (i)

  • Initial Expression: $2 \times 10^3$
  • Step 1 (Expansion of powers of 10): $= 2 \times 10 \times 10 \times 10$
  • Step 2 (Evaluation of base 10 power): $= 2 \times 1000$
  • Final Evaluated Numerical Value: $= 2000$

• Problem (ii)

  • Initial Expression: $7^2 \times 2^3$
  • Step 1 (Expansion of exponential terms): $= 7 \times 7 \times 2 \times 2 \times 2$
  • Step 2 (Intermediate multiplication of squared and cubed bases): $= 49 \times 8$
  • Final Evaluated Numerical Value: $= 392$

• Problem (iii)

  • Initial Expression: $3 \times 4^4$
  • Step 1 (Expansion of exponential base 4 term): $= 3 \times 4 \times 4 \times 4 \times 4$
  • Step 2 (Evaluation of $4^4$): $= 3 \times 256$
  • Final Evaluated Numerical Value: $= 768$

• Problem (iv)

  • Initial Problem Statement Header: $(-3)^2 + (-5)^2$
  • Step 1 (Calculated multiplicative expansion of negative terms): $= (-3) \times (-3) \times (-5) \times (-5)$
  • Step 2 (Evaluation of squared negative numbers): $= 9 \times 25$
  • Final Evaluated Numerical Value: $= 225$