Question

HELLO♥️
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My todays questions = SOLVE THE FOLLOWING
a.
$({9}^{3} - {7}^{3} )\times ( {7}^{3} - {4}^{3} )$
b.
${6}^{3} \div {6}^{2}$
c.
$\sqrt[3]{2197} - 10$
d.
${8}^{3} + {7}^{3} + {6}^{3} + {5}^{3} + {4}^{3} - (630 \times 2)$
e.
$1800 \div 10 ((12 - 6) \div (24 - 12))$
f.
$(9 - 5 {)}^{3} \div (15 - 6 {)}^{3}$
g.
$( - 16 {)}^{3}$
h.
$\sqrt[3]{1000000}$
i. last
$({3}^{3 {)}^{3} }$
plz plz plzzz solve these question is u know anyone plzzzzzzzzz big request to u plzzz itz my test tomorrow​

Answer 1

Solution

(1)

$\frac{9 {}^{3} - 7 {}^{3} }{7 {}^{3} - 4 {}^{3} } \\ = \frac{(9 - 7)(9 {}^{2} + 7 {}^{2} + 9 \times 7) }{(7 - 4)(7 {}^{2} + 4 {}^{2} + 4 \times 7)} \\ = \frac{2 \times (81 + 49 + 63)}{3(49 + 16 + 28)} \\ = \frac{2 \times 193}{ 3 \times 93} \\ = \frac{386}{279}$

(2)

$\frac{6 {}^{3} }{6 {}^{2} } = 6 {}^{3 - 2} = 6 {}^{1} = 6$

(3)

$\sqrt[3]{2197} - 10 \\ = \sqrt[3]{13 \times 13 \times 13} - 10 \\ = 13 - 10 = 3$

(4)

$8 {}^{3} + 7 {}^{3} + 6 {}^{3} + 5 {}^{3} + 4 {}^{3} - (630 \times 2) \\ = 512 + 343 + 216 + 125 + 64 - 1260 \\ = 1260 - 1260 = 0$

(5)

$1800 \div 10 ((12 - 6) \div (24 - 12)) \: \\ = 1800 \div10(6 \div12) \\ = 1800 \div10( \frac{1}{2} ) \\ = 1800 \div5 \\ = 360$

(6)

$(9 - 5 {)}^{3} \div (15 - 6 {)}^{3} \: \\ = \frac{4 {}^{3} }{9 {}^{3} } \\ = \frac{64}{729}$

(7)

$( - 16 {)}^{3} \: \\ = ( - 1 ) {}^{3} \times (16) {}^{3} \\ = - (4 \times 4) {}^{3} \\ = - 4{}^{3 } \times 4 {}^{3} = - 64 \times 64 = - 4096$

(8)

$\sqrt[3]{1000000} \\ = \sqrt[3]{100 \times 100 \times 100} \\ = 100$

(9)

${3}^{3 {}^{3} }\\ = 3 {}^{27} \\ or \\ (3 {}^{3} ) {}^{3} = 3 {}^{3 \times 3} = 3 {}^{9}$

Hope this help u .........xd