Question

Rewrite the expression with positive exponents. $$(-10 a)^{0}$$

Short answer

The simplified expression is 1, provided that \(a\) is not zero. If \(a\) is zero, the expression is undefined.

Step-by-step solution

Analyze the base and exponent

Here we have an expression with a base of \(-10a\) and an exponent of 0. The base is not 0 (unless \(a\) is equal to 0), so the expression is well defined.

Use the rule for zero exponent

The rule of exponents states that any non-zero number raised to the power of zero is equal to 1. So, we simplify \((-10a)^{0}\) to 1, provided that \(a\) is not zero.

Write the simplified expression

Following the rule applied in Step 2, the simplified expression is 1, as long as \(a\) is not zero. If \(a\) is zero, then the expression is undefined because we have a 0 base to a 0 power.