What number has the prime factorization #2^3 \times 5^2 \times 7# ? How did you find the number?

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Answer 1 · 2018-03-07T07:34:35

#1400#

Given: prime factorization #2^3 xx 5^2 xx 7#

#2^3 xx 5^2 xx 7 = 2 xx 2 xx 2 xx 5 xx 5 xx 7#

#= 8 xx 25 xx 7 = 200 xx 7 = 1400#

Answer 2 · 2018-03-07T07:55:59

#2^3×5^2×7# equals #1400#

#2^3×5^2×7# equals what number?

You find the number by multiplying all its factors together.

#2^3 × 5^2 ×7#

#color(white)(.)##8 × 25 × 7#

#color(white)(.)# ╲ ╱ #darr#

#color(white)(.)# #200 xx 7#

#color(white)(......)# ╲ ╱

#color(white)(......)# 1400

#color(white)(............)#――――――

Check

Factor #1400# into its prime factors and see if that brings back the same factors that were in the original question.

#color(white)(......)# 1400

#color(white)(......)# ╱ ╲

#color(white)(m)# #14 xx 100#

#color(white)(m)#╱ ╲ ╱ ╲

#color(white)()# #2 xx 7 xx 2 xx 50#

#darr# #darr# #darr# ╱ ╲

#color(white)(.)##2 xx7 xx 2 xx 2 xx 25#

#darr# #darr# #darr# #darr# ╱ ╲

#color(white)(.)##2 xx7 xx 2 xx 2 xx 5 xx 5#

#2^3 xx 5^2 xx 7 #

#Check#