What is (rs)^3(2s)^{-2}(4r)^4 ?

The solution to (rs)^3(2s)^{-2}(4r)^4 is 64r^7s

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simplify (rs)^3(2s)^{-2}(4r)^4

simplify

(rs)^{3} (2 s)^{- 2} (4 r)^{4}

64 r^{7} s

Solution steps

(rs)^{3} (2 s)^{- 2} (4 r)^{4}

Apply exponent rule:

(a \cdot b)^{n} = a^{n} b^{n}

(rs)^{3} = r^{3} s^{3}

= r^{3} s^{3} (2 s)^{- 2} (4 r)^{4}

Simplify

(2 s)^{- 2} : \frac{1}{4 s ^{2}}

= r^{3} s^{3} \frac{1}{4 s ^{2}} (4 r)^{4}

Simplify

(4 r)^{4} : 256 r^{4}

= r^{3} s^{3} \frac{1}{4 s ^{2}} \cdot 256 r^{4}

Simplify

r^{3} r^{4} : r^{7}

= r^{7} s^{3} \frac{1}{4 s ^{2}} \cdot 256

= 256 r^{7} s^{3} \frac{1}{4 s ^{2}}

Apply the fraction rule:

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

= \frac{256 r ^{7} s ^{3} \cdot 1}{4 s ^{2}}

Multiply the numbers:

256 \cdot 1 = 256

= \frac{256 r ^{7} s ^{3}}{4 s ^{2}}

Factor the number:

256 = 4 \cdot 64

= \frac{4 \cdot 64 r ^{7} s ^{3}}{4 s ^{2}}

Cancel the common factor:

4

= \frac{64 r ^{7} s ^{3}}{s ^{2}}

Simplify

\frac{s ^{3}}{s ^{2}} : s

= 64 r^{7} s

\frac{5}{14}

(x - 10) (x - 10)

\frac{15}{3}

4 - \frac{2}{7}

(x + 1)^{2} (x + 2)^{2}