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Chapter 8: Q. 55 (page 771)

In the following exercises, use the Product Property to simplify radical expression27.

Short Answer

Expert verified

The radical expression in simplified form is33.

Step by step solution

01

Step 1. Given Information

The given expression is 27.

We have to use the Product Property to simplify the radical expression.

02

Step 2. Use the product rule to rewrite the radical as the product of two radicals

By using the rule we get,

9·3

03

Step 3. Simplify the root of the perfect power

By simplifying we get,

9·3=33

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Most popular questions from this chapter

In the following exercises, write with a rational exponent.

(a)a3(b)(21v4)3(c)2xy5z24

Simplify:

a-643b-814.

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, solve.
u-3-3=u

Simplify:

a.81n2532b.a32b1243
See all solutions

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