Mathematics, 16.12.2019 19:31, BreBreDoeCCx
Which expression is equivalent to rootindex 3 startroot startfraction 75 a superscript 7 baseline b superscript 4 baseline over 40 a superscript 13 baseline c superscript 9 baseline endfraction endroot? assume a not-equals 0 and c not-equals 0.
a. startfraction a cubed b (rootindex 3 startroot 15 b squared endroot) over 2 c cubed endfraction
b. startfraction b (rootindex 3 startroot 15 b endroot) over 2 a squared c cubed endfraction
c. startfraction a cubed b (rootindex 3 startroot 15 b squared endroot) over 6 c cubed endfraction
d. startfraction b (rootindex 3 startroot 15 b endroot) over 2 a c endfraction
Answers: 2
![\frac{b}{2a^{2}c^3}\sqrt[3]{15b}](/tpl/images/0420/9204/f4ee7.png)
![\sqrt[3]{\frac{75a^7b^4}{40a^{13}c^9}}](/tpl/images/0420/9204/66220.png)
to simplest form, we get:
![\sqrt[3]{\frac{15(a^{-2})^3\times b\times b^3}{2^3(c^3)^3}}](/tpl/images/0420/9204/e647b.png)
![\sqrt[3]{x^3} =x](/tpl/images/0420/9204/aa9ac.png)
. Thus, the expression becomes:![\frac{a^{-2}b}{2c^3}\sqrt[3]{15b}](/tpl/images/0420/9204/4e94e.png)
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