Exponents & Logarithms

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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…]

Using Exponents to Simplify Equations

An exponent is a small, superscripted number written above and to the right of a larger number, the base — this tells you how many times you multiply the base by itself. This repeated multiplication is [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 use in computations. To write in scientific notation, follow the form [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) with the same base, subtract the exponents. Division [more…]

How to Divide with the Power of Zero

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How to Add and Subtract with Powers

To add or subtract with powers, both the variables and the exponents of the variables must be the same. You perform the required operations on the coefficients, leaving the variable and exponent as they [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 it as a number between [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 Raise Powers of Powers

When raising a power to a power in an exponential expression, you find the new power by multiplying the two powers together. For example, in the following expression, x to the power of 3 is being raised [more…]

Working 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 Simplify Negative Exponents with Variables

Distributing with negative exponents means that you'll have fractional answers. A base that has a negative exponent can be changed to a fraction. The base and the exponent become the denominator, but the [more…]

Rules of Exponents

Exponents are shorthand for repeated multiplication. The rules for performing operations involving exponents allow you to change multiplication and division expressions with the same base to something [more…]

Logarithm Basics

Logarithms are simply another way to write exponents. Exponential and logarithmic functions are inverses of each other. For solving and graphing logarithmic functions [more…]

Algebra: Rules of Exponents

Exponents are shorthand for repeated multiplication. The rules for performing operations involving exponents allow you to change multiplication and division expressions with the same base into something [more…]

Algebra II: What Is the Binomial Theorem?

A binomial is a mathematical expression that has two terms. In algebra, people frequently raise binomials to powers to complete computations. The binomial theorem says that if [more…]

Algebra II: Raise Binomials to a Power

A binomial is a mathematical expression that has two terms. In algebra, people frequently raise binomials to powers in order to solve equations. Here are some examples: [more…]

Exponential Systems

You can solve systems of exponential equations algebraically when the bases of the exponential terms are the same number or when obvious (don’t you hate that word in mathematics?) solutions pop out because [more…]

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