(-7a^2b^3c^0/3a^3b^4c^3)^-4

Jasonbradley

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Jun 16, 2024

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Simplifying the Expression (-7a^2b^3c^0/3a^3b^4c^3)^-4

This article will guide you through the steps of simplifying the expression (-7a^2b^3c^0/3a^3b^4c^3)^-4.

Understanding the Properties

Before we begin simplifying, let's recall some important properties of exponents:

• Negative Exponent: x^-n = 1/x^n
• Fractional Exponent: (x/y)^n = x^n / y^n
• Zero Exponent: x^0 = 1

Simplifying the Expression

1. Simplify the numerator:

   • c^0 = 1 (using zero exponent property)

2. Simplify the denominator:

   • Combine the 'a' terms: a^2 / a^3 = a^(2-3) = a^-1
   • Combine the 'b' terms: b^3 / b^4 = b^(3-4) = b^-1

3. Apply the negative exponent property to the entire fraction:

   • (-7a^2b^3/3a^3b^4c^3)^-4 = (3a^3b^4c^3 / -7a^2b^3)^4

4. Simplify inside the parentheses:

   • (3a^3b^4c^3 / -7a^2b^3)^4 = (3/(-7)) * (a^(3-2)) * (b^(4-3)) * (c^3)^4

5. Apply the power of a product rule:

   • (3/(-7)) * (a^(3-2)) * (b^(4-3)) * (c^3)^4 = (-3/7) * a * b * c^12

6. Simplify the final expression:

   • (-3/7) * a * b * c^12 = -3abc^12 / 7

Final Result

Therefore, the simplified form of the expression (-7a^2b^3c^0/3a^3b^4c^3)^-4 is -3abc^12 / 7.