Exponents & Logarithms

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How to Use Exponents

Exponents, those small numbers to the upper right of larger numbers, tell you how many times you multiply the larger number, the base, by itself. This repeated multiplication is commonly referred to as [more…]

How to Compare Numbers by Using Exponents

You can compare number values more easily when you use exponents, because numbers — especially large ones — can be deceiving. To discover the real value of a large number, write that number as a number [more…]

How to Write Numbers in Scientific Notation

Scientific notation is a standard way of writing very large and very small numbers so that they're easier to both compare and to use in computations. To write in scientific notation, follow the form [more…]

How to Solve Problems Using Exponential Expressions

Using exponential expressions to solve problems that involve repeated actions is the best way to find the answer. Exponential expressions help you figure out problems that do the same thing over and over [more…]

How to Multiply Exponents

You can multiply many exponential expressions together without having to change their form into the big or small numbers they represent. When multiplying exponents, the only requirement is that the bases [more…]

How to Divide Exponents

You can divide exponential expressions, leaving the answers as exponential expressions, as long as the bases are the same. To divide exponents (or powers [more…]

How to Divide with the Power of Zero

When you see x0, you may assume that x = 0, but x represents some unknown real number — it just can’t be 0. When you divide with a power of zero, any number raised to the power of zero equals 1, as long [more…]

How to Raise Powers of Powers

An exponential expression, such as (x3)6, is referred to as raising a power to a power. When raising a power to a power in an exponential expression, you find the new power by multiplying the two powers [more…]

How to Work with Negative Exponents

Negative exponents are a way of writing powers of fractions or decimals without using a fraction or decimal. You use negative exponents as a way to combine expressions with the same base, whether the different [more…]

How to Add and Subtract with Powers

To add or subtract with powers, both the variables as well as the exponents of the variables must be the same. Perform the required operations on the coefficients, leaving the variable and exponent as [more…]

Algebra’s Laws of Logarithms

Logarithms help you add instead of multiply. The algebra formulas here make it easy to find equivalence, the logarithm of a product, quotient, power, reciprocal, base, and the log of 1. [more…]