Laws of Exponents

Front

What is the rule for negative exponents?

Back

A negative exponent indicates that the base should be taken as the reciprocal. For example, a^(-n) = 1/(a^n).

Front

How do you simplify (x^3)(x^2)?

Back

You add the exponents: x^(3+2) = x^5.

Front

How do you express 5⋅5⋅5⋅5⋅5⋅5⋅5 using exponents?

Back

It can be written as 5^7.

Front

What is the result of multiplying 10^1 and 10^-2?

Back

10^(1 + (-2)) = 10^(-1) = 1/10.

Front

When multiplying two powers with the same base, what do you do with the exponents?

Back

You add the exponents.

Front

What is the rule for zero exponents?

Back

Any non-zero base raised to the power of zero equals one: a^0 = 1.

Front

How do you simplify (a^m)(a^n)?

Back

You add the exponents: a^(m+n).

Front

What is the result of (x^4)/(x^2)?

Back

You subtract the exponents: x^(4-2) = x^2.

Front

What does a fractional exponent represent?

Back

A fractional exponent represents a root: a^(1/n) = n√a.

Front

How do you express (2^3)^4?

Back

You multiply the exponents: 2^(3*4) = 2^12.