Rational expressions

8b^3/7t^2 * 49t^4/64b

The problem here is your lack of brackets.

People are guessing what you may mean.

Technically, (using the rules of PEDMAS) this is your meaning

$\frac{8b^3}{7}\times t^2 \times \frac{49t^4}{64}\times b$

Heureka has interpreted what he thinks you meant NOT what you wrote down. We commonly do this.

I am not sure what our guests did.

Simplify the following:
(8×49 b^3 t^2 t^4 b)/(7×64)

8/64 = 8/(8×8) = 1/8:
(49 t^4 b b^3 t^2)/(7×8)

49/7 = (7×7)/7 = 7:
(7 t^4 b b^3 t^2)/8

Combine powers. (7 t^4 b b^3 t^2)/8 = (7 t^(4+2) b^(3+1))/8:
(7 t^4+2 b^3+1)/8

4+2 = 6:
(7 t^6 b^(3+1))/8

3+1 = 4:
Answer: | 
| (7t^6 b^4)/8

Multiply and simplify

8b^3/7t^2 * 49t^4/64b

$\begin{array}{rcll} \dfrac{ 8b^3 }{ 7t^2 } \cdot \dfrac{ 49t^4 } { 64b } &=&\dfrac{ 8\cdot b^3 }{ 7\cdot t^2 } \cdot \dfrac{ 49\cdot t^4 } { 64\cdot b } \\\\ &=&\dfrac{ 8\cdot b^3 \cdot 49\cdot t^4 }{ 7\cdot t^2 \cdot 64\cdot b } \\\\ &=&\dfrac{ 49 \cdot 8 \cdot b^3 \cdot t^4 }{ 7\cdot 64\cdot b\cdot t^2 } \\\\ &=& \dfrac{8}{64} \cdot \dfrac{49}{7} \cdot \dfrac{b^3}{b} \cdot \dfrac{t^4}{t^2} \\\\ &=& \dfrac{8}{64} \cdot \dfrac{49}{7} \cdot \dfrac{b^3}{b} \cdot \dfrac{t^4}{t^2} \qquad & | \qquad 49 = 7^2 \qquad 64 = 8^2\\\\ &=& \dfrac{8}{8^2} \cdot \dfrac{7^2}{7} \cdot \dfrac{b^3}{b} \cdot \dfrac{t^4}{t^2} \\\\ &=& \dfrac{1}{8^2\cdot 8^{-1} } \cdot \dfrac{7^2\cdot 7^{-1} }{1} \cdot \dfrac{b^3\cdot b^{-1} }{1} \cdot \dfrac{t^4\cdot t^{-2}}{1} \\\\ &=& \dfrac{1}{8^{2-1} } \cdot \dfrac{7^{2-1} }{1} \cdot \dfrac{b^{3-1} }{1} \cdot \dfrac{t^{4-2}}{1} \\\\ &=& \dfrac{1}{8^{1} } \cdot \dfrac{7^{1} }{1} \cdot \dfrac{b^{2} }{1} \cdot \dfrac{t^{2}}{1} \\\\ &=& \dfrac{1}{8 } \cdot \dfrac{7 }{1} \cdot \dfrac{b^{2} }{1} \cdot \dfrac{t^{2}}{1} \\\\ &=& \dfrac{7\cdot b^{2}\cdot t^{2} }{8 } \\\\ &=& \dfrac{7 b^{2} t^{2} }{8 } \\\\ \end{array}$

CPhill: please rectify the discrepancies. Thanks.

Simplify the following:
(8×49 b^3 t^4)/(7 t^2 64 b)

8/64 = 8/(8×8) = 1/8:
(49 t^4 b^3)/(8×7 b t^2)

49/7 = (7×7)/7 = 7:
(7 t^4 b^3)/(8 b t^2)

Combine powers. (7 t^4 b^3)/(8 b t^2) = (7 t^(4-2) b^(3-1))/8:
(7 t^4-2 b^3-1)/8

4-2 = 2:
(7 t^2 b^(3-1))/8

3-1 = 2:
Answer: | 
| (7t^2 b^2)/8