What is simplify-7/8*a^m*(b^n)/((-3/4))*a*b^2 ?

The solution to simplify-7/8*a^m*(b^n)/((-3/4))*a*b^2 is (7a^{m+1}b^{n+2})/6

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simplify-7/8a^m(b^n)/((-3/4))ab^2

simplify

- \frac{7}{8} \cdot a^{m} \cdot \frac{b ^{n}}{( - \frac{3}{4} )} \cdot a \cdot b^{2}

\frac{7 a ^{m + 1} b ^{n + 2}}{6}

Solution steps

- \frac{7}{8} a^{m} \frac{b ^{n}}{- \frac{3}{4}} a b^{2}

Apply exponent rule:

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

a^{m} a = a^{m + 1}

= - \frac{7}{8} a^{m + 1} \frac{b ^{n}}{- \frac{3}{4}} b^{2}

\frac{b ^{n}}{- \frac{3}{4}} = - \frac{4 b ^{n}}{3}

= - \frac{7}{8} (- \frac{4 b ^{n}}{3}) b^{2} a^{m + 1}

Apply rule

- (- a) = a

= \frac{7}{8} a^{m + 1} \frac{b ^{n} \cdot 4}{3} b^{2}

Multiply fractions:

a \cdot \frac{b}{c} \cdot \frac{d}{e} = \frac{a \cdot b \cdot d}{c \cdot e}

= \frac{7 b ^{n} \cdot 4 a ^{m + 1} b ^{2}}{8 \cdot 3}

7 b^{n} \cdot 4 a^{m + 1} b^{2} = 28 a^{m + 1} b^{n + 2}

= \frac{28 a ^{m + 1} b ^{n + 2}}{8 \cdot 3}

Multiply the numbers:

8 \cdot 3 = 24

= \frac{28 a ^{m + 1} b ^{n + 2}}{24}

Cancel the common factor:

4

= \frac{7 a ^{m + 1} b ^{n + 2}}{6}

\frac{1}{1 - \frac{v ^{2}}{c ^{2}}}

(a - 3 b^{2})^{3}

(5 y^{2})^{2}

2 x^{4} - 2 y^{2} + 2 x^{2} y^{2} - 2

(p + 2) (p - 8)

What is simplify-7/8*a^m*(b^n)/((-3/4))*a*b^2 ?
The solution to simplify-7/8*a^m*(b^n)/((-3/4))*a*b^2 is (7a^{m+1}b^{n+2})/6