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Chapter 8: Q 142E (page 787)

In the following exercises, write with a rational exponent.

Part (a):r74

Part (b): 2pq53

Part (c):12m7n34

Short Answer

Expert verified

Part (a): On writing with a rational exponent is r74.

Part (b): On writing with a rational exponent is 2pq35.

Part (c): On writing with a rational exponent is 12m7n34.

Step by step solution

01

Part (a) Step 1. Write with exponents.

Consider the given expression,

r74

We want to use amn=amnto write each radical in the form amn.

The numerator of the exponent is the exponent, 7.

The denominator of the exponent is the index of the radical, 4.

Therefore, the answer is r74.

02

Part (b) Step 1. Write with exponents.

Consider the given expression,

2pq53

We want to use amn=amnto write each radical in the form amn.

The numerator of the exponent is the exponent, 3.

The denominator of the exponent is the index of the radical, 5.

Therefore, the answer is 2pq35.

03

Part (c) Step 1. Write with exponents.

Consider the given expression,

12m7n34

We want to use amn=amn to write each radical in the form amn.

The numerator of the exponent is the exponent, 3.

The denominator of the exponent is the index of the radical, 4.

Therefore, the answer is 12m7n34.

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Most popular questions from this chapter

Simplify:

(a)432

(b)27-23

(c) 625-34

In the following exercises, simplify.

(a) 2532

(b) 9-32

(c)-6423

In the following exercises, simplify using absolute value signs as needed.125r13,108x53,48y64

Explain whyx4=x2{"x":[[79,82,83,87,91,93,93,95,97,99,100,103,103,104,104,104,105,106,109,116,127,145,161,175,183,186,187],[106,107,108,109,110,111,113,115,118,121,122,126,128,128,128,127,124,119,115,114,112,112,111,111,110,110,110],[141,138,135,134,132,130,129,128,128,128,129,130,132,134,137,142,145,148,149,150,151,151],[119,120,123,129,133,136,137],[153,154,154,156,156,157,157,157,157,157,157,156,156,156,156,156,156,156,156,156,156,156,155,154,152,150,149,149,148,149,149,154,162,170,178,179,180,180,179],[185,186,186,187,191,194,197,199,200,201],[183,184,185,189,195,202,206,208],[229,230,232,236,239,244,249,252,254,256,256,256,255,252,250,249,248,247,245,242,240,238],[264,264,262,261,261,261,260,260,260,260,260,261,262,264,268,272,281,286,289,289,289],[245,246,250,259,269,279,288,289,290,291],[277,281,281,282,283,283,283,283,283,283,283,282,285,289,296,303,308,309,309]],"y":[[105,107,109,112,115,116,117,112,103,93,81,69,55,48,45,44,44,43,42,41,40,38,35,32,31,29,29],[71,71,71,70,70,69,68,68,68,68,68,70,74,78,83,88,92,95,97,98,98,99,99,98,96,94,92],[65,65,68,71,75,79,83,87,89,92,96,98,101,104,105,105,105,103,101,99,98,97],[83,83,83,83,83,83,83],[52,53,54,57,61,66,70,75,76,77,76,74,71,66,62,59,57,56,55,54,53,52,52,54,58,60,62,63,64,64,65,65,65,63,62,60,60,61,61],[87,87,86,85,85,84,84,84,84,84],[98,97,97,96,95,94,92,92],[66,66,65,65,65,65,67,70,73,77,82,87,91,95,97,98,99,99,99,99,97,97],[66,65,65,67,70,73,78,82,86,90,93,95,97,98,99,99,98,95,93,92,91],[85,85,85,84,83,81,81,81,81,81],[49,49,50,50,52,56,58,60,62,63,64,64,65,65,65,64,63,62,63]],"t":[[0,26,43,60,76,94,126,159,177,193,209,227,243,260,276,292,309,327,343,359,376,392,409,426,442,459,475],[942,947,959,975,1000,1043,1059,1075,1092,1108,1125,1142,1159,1175,1192,1209,1225,1242,1259,1275,1292,1308,1345,1363,1375,1392,1399],[1736,1791,1807,1824,1842,1858,1875,1891,1908,1924,1941,1958,1974,1991,2008,2025,2041,2058,2074,2091,2108,2123],[2491,2520,2540,2557,2574,2590,2607],[3144,3217,3225,3239,3256,3272,3289,3305,3323,3388,3409,3424,3439,3455,3472,3489,3506,3522,3540,3556,3573,3605,3656,3672,3689,3705,3722,3739,3755,3899,3904,3922,3939,3955,3972,3988,4005,4107,4110],[4450,4455,4471,4488,4504,4521,4538,4554,4571,4607],[4831,4854,4870,4888,4904,4921,4937,4954],[5378,5403,5420,5437,5453,5470,5487,5503,5520,5537,5554,5570,5587,5604,5620,5636,5653,5671,5687,5704,5720,5724],[6030,6086,6102,6119,6136,6153,6170,6186,6202,6219,6237,6252,6270,6286,6303,6319,6336,6352,6370,6386,6391],[6718,6752,6769,6786,6802,6819,6836,6852,6868,6885],[7431,7441,7447,7453,7468,7485,7501,7518,7534,7551,7584,7601,7651,7668,7684,7701,7717,7734,7850]],"version":"2.0.0"}. Then explain whyx16=x8{"x":[[108,111,115,118,123,128,129,131,133,136,139,144,146,147,147,147,148,150,151,153,157,164,176,196,217,241,254,258,259],[177,179,181,185,188,192,195,197,199,200,200,199,193,185,178,172,170,169,168],[241,239,234,229,222,216,211,208,205,204,204,204,205,209,217,226,236,245,251,254],[189,190,194,203,211,216,218,218],[249,250,250,250,250,249,249,248,248],[270,269,268,267,266,265,265,265,265,265,265,267,268,270,273,276,278,280,280,280,280,280,280,278,277,274,271,270,270,269,269,269],[295,298,303,312,321,327,330,331],[303,304,307,311,314,318,320,322,323],[347,349,353,359,363,365,367,368,368,365,361,360,359,358,359],[387,386,383,378,373,367,364,361,360,360,360,362,369,374,380,383,384,384],[347,348,349,351,361,372,382,388,390],[403,404,407,410,411,413,414,414,415,415,413,410,408,406,406,406,405,405,405,407,408,409,411,412,412,412,412,412,409,407,405,404,403,403,402,401,401,401,401,401,401,403,405]],"y":[[170,170,173,175,179,182,184,184,180,173,162,145,129,112,96,83,74,70,69,68,68,68,68,68,68,66,64,63,63],[118,118,116,116,116,116,116,119,124,130,137,144,151,156,159,161,161,161,161],[110,110,112,115,120,126,132,138,143,148,152,155,157,158,159,159,156,152,149,148],[137,137,137,137,137,137,137,138],[75,77,80,86,90,95,99,101,103],[70,70,70,72,75,80,85,89,93,97,98,101,102,102,102,101,99,97,95,94,91,90,89,88,87,87,87,87,88,88,89,90],[121,121,121,121,120,119,118,118],[143,143,143,143,142,141,141,141,141],[111,111,110,110,111,115,119,125,134,140,143,145,145,140,136],[104,104,105,109,114,119,125,129,133,136,138,140,141,141,140,138,136,135],[127,126,126,126,125,124,123,122,122],[85,85,84,84,84,84,85,88,92,95,99,102,105,107,109,110,111,112,113,113,113,113,112,110,108,105,103,100,99,97,96,95,95,94,94,92,91,90,88,86,85,84,84]],"t":[[0,50,67,83,100,117,133,150,199,216,233,249,267,284,299,316,334,350,366,383,400,417,434,449,466,484,500,516,534],[1057,1065,1082,1099,1116,1132,1148,1165,1183,1200,1216,1232,1249,1265,1282,1299,1316,1333,1371],[1674,1682,1698,1715,1731,1748,1765,1782,1799,1815,1831,1849,1865,1881,1898,1915,1932,1948,1965,1975],[2386,2414,2431,2448,2464,2481,2497,2549],[2961,3014,3030,3047,3063,3080,3097,3113,3129],[3496,3523,3533,3546,3563,3579,3596,3613,3629,3647,3663,3680,3696,3713,3729,3746,3762,3779,3796,3813,3830,3846,3862,3879,3896,3913,3930,3945,3962,3979,3995,4012],[4562,4567,4578,4596,4612,4628,4645,4661],[4950,5023,5044,5062,5078,5096,5111,5127,5135],[5454,5461,5477,5494,5511,5527,5544,5561,5577,5594,5610,5627,5644,5694,5707],[5900,5910,5926,5943,5960,5977,5994,6010,6027,6043,6060,6076,6094,6109,6127,6143,6160,6163],[6436,6441,6445,6460,6477,6493,6510,6526,6543],[6953,6960,6975,6992,7009,7025,7042,7059,7076,7093,7108,7125,7142,7159,7175,7193,7209,7225,7247,7259,7276,7292,7308,7325,7342,7358,7375,7392,7408,7425,7441,7459,7515,7524,7541,7558,7575,7593,7608,7625,7643,7658,7669]],"version":"2.0.0"}.

In the following exercises, write with a rational exponent.

鈸�x7鈸�y9鈸�f5
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