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Example text

1 / 4 is )1/ 4 ≠ −2. ( −2 ⋅ −2 ⋅ −2 ⋅ −2 = 16, not −16. ( − )1 / 4 = 4 −16 is not defined for real numbers. ⎛ 32 ⎞ d. ⎜ − ⎝ 243 ⎟⎠ 1/ 5 Step 1. Apply x1 / n ⎛ 32 ⎞ − ⎝ 243 ⎠ n x. 1/5 =5− 32 243 Step 2. Find the principal fifth root of − ⎛ 32 ⎞ − ⎝ 243 ⎠ P 1/5 =5− 32 . 243 32 2 =− 243 3 When you evaluate exponential expressions that have unit fraction exponents, you should practice doing Step 1 mentally. For instance, 491 / 2 ⎛ 1⎞ ⎜⎝ 32 ⎟⎠ =7, 1/ 5 = ( )1 / 3 = −2, 1 , and so forth. 2 Rational Exponents If x is a real number and m and n are natural numbers, then (a) x m / n (x / n )m or (b) x m / n (x m ) / n, provided that in all cases even roots of negative numbers do not occur.

A. ( )0 b. 6)0 ⎛ 3⎞ c. ⎜ ⎟ ⎝ 4⎠ 0 d. π 0 e. 10 Solution a. ( )0 Step 1. The exponent is 0, so the answer is 1. ( − )0 = 1 b. 6)0 Step 1. The exponent is 0, so the answer is 1. 6)0 = 1 ⎛ 3⎞ c. ⎜ ⎟ ⎝ 4⎠ 0 Step 1. The exponent is 0, so the answer is 1. 0 ⎛ 3⎞ =1 ⎝ 4⎠ d. π 0 Step 1. The exponent is 0, so the answer is 1. π0 = 1 e. 10 Step 1. The exponent is 0, so the answer is 1. 10 1 49 50 Easy Algebra Step-by-Step P Negative Integer Exponents If x is a nonzero real number and n is a natural number, then x − n = A negative integer exponent on a nonzero number tells you to obtain the reciprocal of the corresponding exponential expression that has a positive exponent.

1/5 =5− 32 243 Step 2. Find the principal fifth root of − ⎛ 32 ⎞ − ⎝ 243 ⎠ P 1/5 =5− 32 . 243 32 2 =− 243 3 When you evaluate exponential expressions that have unit fraction exponents, you should practice doing Step 1 mentally. For instance, 491 / 2 ⎛ 1⎞ ⎜⎝ 32 ⎟⎠ =7, 1/ 5 = ( )1 / 3 = −2, 1 , and so forth. 2 Rational Exponents If x is a real number and m and n are natural numbers, then (a) x m / n (x / n )m or (b) x m / n (x m ) / n, provided that in all cases even roots of negative numbers do not occur.

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