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Polynomials and Radicals Help (page 4)

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Updated on Oct 27, 2011

Exponents

When a value, or base, is raised to a power, that power is the exponent of the base. The exponent of the term 42 is 2, and the base of the term is 4. The exponent is equal to the number of times a base is multiplied by itself: 42 = (4)(4); 26 = (2)(2)(2)(2)(2)(2).

Tip: Any value with an exponent of 0 is equal to 1: 10 = 1, 100 = 1, x0 = 1.

Tip: Any value with an exponent of 1 is equal to itself: 11 = 1, 101 = 10, x1 = x.

Fractional Exponents

An exponent can also be a fraction. The numerator of the fraction is the power to which the base is being raised. The denominator of the fraction is the root of the base that must be taken. For example, the square root of a number can be represented as , which means that x must be raised to the first power (x1 = x) and then the second, or square, root must be taken: = √x.

= (√4)3 = 23 = 8

It does not matter if you find the root (represented by the denominator) first, and then raise the result to the power (represented by the numerator), or if you find the power first and then take the root.

= (√4)3 = 64, √64 = 8

Negative Exponents

A base raised to a negative exponent is equal to the reciprocal of the base raised to the positive value of that exponent.

3–3 =

x–2 =

Multiplying and Dividing Terms with Exponents

To multiply two terms with common bases, multiply the coefficients of the bases and add the exponents of the bases.

(3x2)(7x4) = 21x6

(2x–5)(2x3) = 4x–2, or

(xc)(xd) = xc + d

To divide two terms with common bases, divide the coefficients of the bases and subtract the exponents of the bases.

= 3x4

= x cd

Raising a Term with an Exponent to Another Exponent

When a term with an exponent is raised to another exponent, keep the base of the term and multiply the exponents.

(x3)3 = x9

(xc)d = xcd

If the term that is being raised to an exponent has a coefficient, be sure to raise the coefficient to the exponent as well.

(3x2)3 = 27x6

(cx3)4 = c4x12

Find practice problems and solutions for these concepts at Polynomials and Radicals Practice Problems.

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