What is (32a^7b^5+48a^6b^4-a^4b^3)/(8ab^3) ?

The solution to (32a^7b^5+48a^6b^4-a^4b^3)/(8ab^3) is (a^3(32a^3b^2+48a^2b-1))/8

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simplify (32a^7b^5+48a^6b^4-a^4b^3)/(8ab^3)

simplify

\frac{32 a ^{7} b ^{5} + 48 a ^{6} b ^{4} - a ^{4} b ^{3}}{8 a b ^{3}}

\frac{a ^{3} ( 32 a ^{3} b ^{2} + 48 a ^{2} b - 1 )}{8}

Solution steps

\frac{32 a ^{7} b ^{5} + 48 a ^{6} b ^{4} - a ^{4} b ^{3}}{8 a b ^{3}}

Factor

32 a^{7} b^{5} + 48 a^{6} b^{4} - a^{4} b^{3} : a^{4} b^{3} (32 a^{3} b^{2} + 48 a^{2} b - 1)

= \frac{a ^{4} b ^{3} ( 32 a ^{3} b ^{2} + 48 a ^{2} b - 1 )}{8 a b ^{3}}

Cancel the common factor:

b^{3}

= \frac{a ^{4} ( 32 a ^{3} b ^{2} + 48 a ^{2} b - 1 )}{8 a}

Apply exponent rule:

a^{b + c} = a^{b} \cdot a^{c}

a^{4} = a a^{3}

= \frac{a a ^{3} ( 32 a ^{3} b ^{2} + 48 a ^{2} b - 1 )}{8 a}

Cancel the common factor:

a

= \frac{a ^{3} ( 32 a ^{3} b ^{2} + 48 a ^{2} b - 1 )}{8}

(s - 2)^{4}

\frac{3}{2} - \frac{9}{2}

6 2^{2}

6 x^{4} + x^{3} + 5 x^{2} + x - 1

- 4 (3 d - 2) - 7

What is (32a^7b^5+48a^6b^4-a^4b^3)/(8ab^3) ?
The solution to (32a^7b^5+48a^6b^4-a^4b^3)/(8ab^3) is (a^3(32a^3b^2+48a^2b-1))/8