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In the following equation, what is the value of zz?\newline62=6z636^2 = \frac{6^z}{6^3}\newlinez=z = ____

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Full solution

Q. In the following equation, what is the value of zz?\newline62=6z636^2 = \frac{6^z}{6^3}\newlinez=z = ____
  1. Simplify Exponents: Simplify the right side of the equation using the properties of exponents: 6z63=6z−3\frac{6^z}{6^3} = 6^{z-3}.
  2. Set Equal: Set the simplified equation equal to the left side: 62=6z−36^2 = 6^{z-3}.
  3. Base Equality: Since the bases are the same 66, set the exponents equal to each other: 2=z−32 = z - 3.
  4. Solve for z: Solve for z: z=2+3z = 2 + 3.
  5. Calculate z: Calculate z: z=5z = 5.

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