Pasimplehin ito sqrt (9 ^ (16x ^ 2))?

Sagot:

#sqrt (9 ^ (16x ^ 2)) = 9 ^ (8x ^ 2) = 43,046,721 ^ (x ^ 2) #

(sa pag-aakala gusto mo lamang ang pangunahing square root)

Paliwanag:

Mula noon # b ^ (2m) = (b ^ m) ^ 2 #

#sqrt (9 ^ (16x ^ 2)) = sqrt ((9 ^ (8x ^ 2)) ^ 2) #

#color (white) ("XXX") = 9 ^ (8x ^ 2) #

#color (white) ("XXX") = (9 ^ 8) ^ (x ^ 2) #

#color (puti) ("XXX") = 43,046,721 ^ (x ^ 2) #

Sagot:

# 3 ^ (16x ^ 2) # o # 9 ^ (8x ^ 2) #

Paliwanag:

#sqrt (9 ^ (16x ^ 2)) = (9 ^ (16x ^ 2)) ^ (1/2) = 9 ^ ((1/2) 16x ^ 2) #

# = (9 ^ (1/2)) ^ (16x ^ 2) = 3 ^ (16x ^ 2) # O # = 9 ^ ((1/2 * 16) x ^ 2) = 9 ^ (8x ^ 2) #

Sagot:

# 3 ^ (16x ^ 2) #

Paliwanag:

Maaari mong gawing simple ang expression na ito gamit ang iba't ibang mga katangian ng radicals at exponents. Halimbawa, alam mo iyan

#color (asul) (sqrt (x) = x ^ (1/2)) "" # at # "" kulay (asul) ((x ^ a) ^ b = x ^ (a * b)) #

Sa kasong ito, makakakuha ka

(9 ^ (16x ^ 2)) = 9 ^ (16x ^ 2) ^ (1/2) = 9 ^ (16x ^ 2 * 1/2) = 9 ^ (8x ^ 2)

Dahil alam mo iyan #9 = 3^2#, maaari mong muling isulat ito bilang

# 9 ^ (8x ^ 2) = (3 ^ 2) ^ (8x ^ 2) = 3 ^ (16x ^ 2) #

Ang isa pang diskarte na maaari mong gamitin ay

#sqrt (9 ^ (16x ^ 2)) = sqrt ((9 ^ (8x ^ 2)) ^ 2) = 9 ^ (8x ^ 2) = 3 ^ (16x ^ 2)

Bilang kahalili, maaari mo ring gamitin

# ^ ^ (9 ^ (16x ^ 2)) = sqrt ((9 ^ (x ^ 2)) ^ 16) = (9 ^ (x ^ 2)) ^ 8 = (3 ^ 2) ^ (x ^ 2) ^ 8 = 3 ^ (16x ^ 2) #