Scientific Notation: Powers and Roots

Raising Scientific Notation to a Power

When a number in scientific notation is raised to a power, both the coefficient and the exponent are affected. The coefficient is raised to the given power, and the exponent is multiplied by that power.

• Scientific Notation Format: A number is written as a × 10n, where a is the coefficient and n is the exponent.

• Rule: To raise a × 10n to the power of m:

• Example:

Taking Roots of Scientific Notation

When taking the nth root of a number in scientific notation, raise the coefficient to the reciprocal of the root and multiply the exponent by that reciprocal.

• Rule: To take the nth root of a × 10n:

• Example:

Combined Example: Applying Powers and Roots

To solve problems involving both powers and roots in scientific notation, apply the rules step by step to each part of the expression.

• Example: Calculate the following:

• First, calculate each part separately:

• Then, divide the results:

• Final Answer: (rounded as shown in the original notes)

Key Points to Remember

• When raising to a power: raise the coefficient to the power and multiply the exponent by the power.

• When taking a root: raise the coefficient to the reciprocal of the root and divide the exponent by the root.

• Always express the final answer in proper scientific notation.