Evaluate Expressions With Exponents

Evaluate expressions with exponents

When an expression contains exponents, first substitute the given value for each variable, then evaluate the powers, and finally simplify the result.

1) Replace the variable(s)

If you see a variable like (x) or (a), put the given number in its place. Keep parentheses if the value is negative, because they show the base clearly.

2) Evaluate the exponent

An exponent tells you how many times to multiply the base by itself. For example, (3^4 = 3\cdot3\cdot3\cdot3). If the base is negative, be careful:

• ((-2)^4) is positive because the negative is included in the base.
• (-2^4) means the exponent applies before the negative sign.

3) Simplify the expression

Carry out any multiplication or division that remains. If there are several operations, follow the usual order of operations after the powers are found.

Quick check

Ask yourself:

• Did I substitute the value everywhere it appears?
• Did I keep negative bases in parentheses?
• Did I compute the power before any other operation?

Example idea

If (x=2), then (x^3+1 = 2^3+1 = 8+1 = 9). Always recheck your power and sign handling, since most mistakes come from those two steps.