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Zorluk: KolayOperations with Variable Exponents

A square metal plate has a side length of 3x43x^4 centimeters. Which of the following expressions represents the area of the plate in square centimeters?

  1. 9x89x^8Cevap
  2. B
    6x86x^8
  3. C
    9x69x^6
  4. D
    3x83x^8

Cevap

9x89x^8
The area of a square is calculated by squaring its side length. When squaring a term like 3x43x^4, the power of a product rule states that both the coefficient and the variable must be raised to the second power. Squaring the coefficient 3 yields 9, and raising x4x^4 to the second power requires multiplying the exponents (4×2=84 \times 2 = 8), resulting in a final area of 9x89x^8.

Adım Adım Çözüm

1
Recall the formula for the area of a square.
A=s2A = s^2
To find the area, the side length must be squared.
2
Substitute the given side length into the area formula.
A=(3x4)2A = (3x^4)^2
This sets up the mathematical expression that needs to be simplified.
3
Apply the power of a product rule and power of a power rule.
32⋅(x4)2=9x83^2 \cdot (x^4)^2 = 9x^8
The outer exponent (2) must be applied to both the numerical coefficient (32=93^2=9) and the variable exponent (4×2=84 \times 2 = 8).

Anahtar Kavram

Power of a Product and Power of a Power rules
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Konular

Operations with Variable Exponents

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