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This text provides examples and explanations of the different properties of exponents, such as the product of powers property, power of a power property, quotient of powers property, negative exponent property, and zero exponent property. The text also includes practice problems to evaluate powers and simplify expressions using these properties.
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= b–4 +6+7 = b9 r–2–3 ( r – 2 )–3 ( s3 )–3 = b. s3 r 6 = s–9 c. 16m4n –5 2n–5 EXAMPLE 3 Simplify expressions Product of powers property a. b–4b6b7 Power of a quotient property Power of a power property = r6s9 Negative exponent property Quotient of powers property = 8m4n – 5 – (–5) = 8m4n0= 8m4 Zero exponent property
(x–3)2(y3)2 (x–3y3)2 = x5y6 x5y6 x –6y6 = x5y6 EXAMPLE 4 Standardized Test Practice SOLUTION Power of a product property Power of a power property
= x–111 1 = x11 The correct answer is B. ANSWER EXAMPLE 4 Standardized Test Practice = x – 6– 5y6– 6 Quotient of powers property = x–11y 0 Simplify exponents. Zero exponent property Negative exponent property
Astronomy Betelgeuse is one of the stars found in the constellation Orion. Its radius is about 1500 times the radius of the sun. How many times as great as the sun’s volume is Betelgeuse’s volume? EXAMPLE 5 Compare real-life volumes
4 π (1500r)3 Betelgeuse’s volume The volume of a sphere is πr3. 3 = 4 Sun’s volume 4 πr3 3 3 4 π15003r3 3 = 4 πr3 3 EXAMPLE 5 Compare real-life volumes SOLUTION Let r represent the sun’s radius. Then 1500r represents Betelgeuse’s radius. Power of a product property
= 150031 Betelgeuse’s volume is about 3.4 billiontimes as great as the sun’s volume. ANSWER EXAMPLE 5 Compare real-life volumes = 15003r0 Quotient of powers property Zero exponent property = 3,375,000,000 Evaluate power.
for Examples 3, 4, and 5 GUIDED PRACTICE Simplify the expression. Tell which properties of exponents you used. 5. x–6x5 x3 SOLUTION x–6x5x3 = x–6x5 + 3 Power of a product property = x2 Simplify exponents.
= 7z4 y2 for Examples 3, 4, and 5 GUIDED PRACTICE 6. (7y2z5)(y–4z–1) SOLUTION (7y2z5)(y–4z–1) = (7y2z5)(y–4z–1) Power of a product property = (7y2 – 4)(z5 +(–1)) Simplify = (7y–2)(z4) Negative exponent property
s 3 2 s 3 2 7. t–4 t–4 s (3)2 = (t–4 )2 s6 = t–8 = s6t8 for Examples 3, 4, and 5 GUIDED PRACTICE SOLUTION Power of a product property Evaluate power. Negative exponent property
x4y–2 3 8. x3y6 x4y–2 3 (x4)3 (y–2)3 x3y6 = (x3)3(y6)3 x12y–6 = x9y18 x3 = y24 for Examples 3, 4, and 5 GUIDED PRACTICE SOLUTION Power of a powers property Power of a powers property Power of a Quotient property = x3y–24 Negative exponent property
