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Using Properties of Exponents In Exercises 21-26, simplify each expression.
(a)
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Chapter P Solutions
Bundle: College Algebra, Loose-leaf Version, 10th + WebAssign Printed Access Card for Larson's College Algebra, 10th Edition, Single-Term
- Rewriting with Positive Exponents In Exercises 27-30, rewrite each expression with positive exponents. Simplify, if possible. (a) 4y28y4 (b) z+23z+21arrow_forwardEvaluating an Algebraic Expression In Exercises 15-20, evaluate the expression for the given value of x. 7x2,x=4arrow_forwardEXAMPI E 7 Simplify each expression. Assume that all variables represent positive real numbers. Write all answers using positive exponents only. a8/3a1/3 a? (a) 52/753/7 (b) (52/7)3 (c) (a2/363/2,6 (d) Strategy We will use the product, power, and quotient rules for exponents to simplify each expression. Why The familiar rules for exponents are valid for rational exponents. Solution (a) 52/753/7 = 52/7 + 3/7 Use the rule xmx" = xm + n. 2 3 5 = 55/7 Add: 7 (b) (52/7)3 = 5(2/7)(3) Use the rule (xm)" = xmn. = 56/7 Multiply: 극(3)-극(클) -윽 (c) (a2/3b1/2)6 = (a2/3)6(b1/2)6 = a12/366/2 Use the rule (xy)" = x^y^. Use the rule (xm)" = xmn twice. Simplify the exponents. a8/3a1/3 a? Use the rules xmx" = xm + n ut - n (d) a8/3 + 1/3 – 2 and %3D = a8/3 + 1/3 – 6/3 2 = 3 8 3 = a3/3 1 + 3 %D 3 3 3 = 1. 3arrow_forward
- Considering that a0(-1) = 1; a1(-1) = 3, determine the product form (capital pi expression) of the expression below:arrow_forwardEXAMPLE 1 Simplify each expression. Assume that x can represent any nonzero real number. (a) 64-1/2 (b) (-16)-5/4 (c) -625-3/4 (d) (-32x5)-2/5 and (e) 1 25-3/2 Strategy 1 or x-m/n We will use one of the rules x-m/n 1 xm/n to write the reciprocal of each exponential expression and change the exponent's sign to positive. tm/n Why If we can produce an equivalent expression having a positive rational exponent, we can use the methods of this section to simplify it. Solution 1 Because the exponent is negative, write the reciprocal of 64¬1/2, and change the sign of the 1 (a) 64-1/2 641/2 64 8. exponent. (b) (-16)-5/4 is not a real number because (-16)5/4 is not a real number. (c) In -625-3/4, the base is 1 1 -625- -3/4 625)3 1 1 %3D %3D %D 6253/4 53 125 1 1 (d) (-32x5)-2/5 = 1 %D %D (-32x5)2/5 ¯ (V-32x5)2 (-2x)² 1 (e) -3/2 = 253/2 = (/25)³ = 53 = Because the exponent is negative, write the reciprocal of 1 25-3/2 and change the sign of the 25-3/2' exponent. ||arrow_forwardProficiency #5. [Set Builder Notation] (a) Write the set A = {4,6,7, 8, 9, 11} in set builder notation without using any of the numbers in A. (b) Write “the set of real numbers that are the negative square root of an integer" in set builder notation, without using any words.arrow_forward
- (a) Explain the meaning of the exponent in the expression 23 . (b) Explain the meaning of the exponent in the expression 23 .arrow_forwardDistance The distance between Earth and one of the brightest stars in the night star is 33.7 light years. One light year is about 6,000,000,000,000 (6 trillion), miles. (a) Write the number of miles in one light year in scientific notation. (b) Use scientific notation to find the distance between Earth and the star in miles. Write the answer in scientific notation.arrow_forwardThe Gross Domestic Product (GDP) for the United States in the first quarter of 2014 was 1.714961013 . Rewrite the GDP in standard notation.arrow_forward
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