Question

Write each as a single power.
(53)^3

Answer 1

The expression (53)^3 simplifies to 59 by multiplying the exponents. This rule can be applied directly to the exponents without expanding the base.

Step-by-step explanation:

Writing an expression as a single power simplifies the expression and makes it easier to understand and use in calculations. The expression given, (53)^3, can be simplified by cubing the base 53, and then multiplying the exponents. Following the rule that when you raise a power to a power, you multiply the exponents, the simplification would look like this:

Simplified Expression:

(53)^3 = 53 × 3 = 59.

There's no need to expand 53 as 5×5×5 and then do the cubing. Instead, we can directly multiply the exponent 3 by the outer exponent 3 to get the new exponent, 9, for the base number 5.