What is 15/2 x^4y^{-2}(0.13x^5y^4) ?

The solution to 15/2 x^4y^{-2}(0.13x^5y^4) is (39x^9y^2)/(40)

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simplify 15/2 x^4y^{-2}(0.13x^5y^4)

simplify

\frac{15}{2} x^{4} y^{- 2} (0.13 x^{5} y^{4})

\frac{39 x ^{9} y ^{2}}{40}

Solution steps

\frac{15}{2} x^{4} y^{- 2} (0.13 x^{5} y^{4})

Apply exponent rule:

a^{- b} = \frac{1}{a ^{b}}

y^{- 2} = \frac{1}{y ^{2}}

= \frac{15}{2} x^{4} \frac{1}{y ^{2}} \cdot 0.13 x^{5} y^{4}

Simplify

x^{4} x^{5} : x^{9}

= \frac{15}{2} x^{9} \frac{1}{y ^{2}} \cdot 0.13 y^{4}

= \frac{15}{2} \cdot 0.13 x^{9} y^{4} \frac{1}{y ^{2}}

0.13 = \frac{13}{100}

= \frac{15}{2} \cdot \frac{13}{100} x^{9} y^{4} \frac{1}{y ^{2}}

Apply the fraction rule:

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

= \frac{15 \cdot 13 x ^{9} y ^{4} \cdot 1}{2 \cdot 100 y ^{2}}

Multiply the numbers:

15 \cdot 13 \cdot 1 = 195

= \frac{195 x ^{9} y ^{4}}{2 \cdot 100 y ^{2}}

Factor the number:

195 = 5 \cdot 39

= \frac{5 \cdot 39 x ^{9} y ^{4}}{2 \cdot 100 y ^{2}}

Factor the number:

100 = 5 \cdot 20

= \frac{5 \cdot 39 x ^{9} y ^{4}}{2 \cdot 5 \cdot 20 y ^{2}}

Cancel the common factor:

5

= \frac{39 x ^{9} y ^{4}}{2 \cdot 20 y ^{2}}

Simplify

\frac{y ^{4}}{y ^{2}} : y^{2}

= \frac{39 x ^{9} y ^{2}}{2 \cdot 20}

Multiply the numbers:

2 \cdot 20 = 40

= \frac{39 x ^{9} y ^{2}}{40}

e^{- \frac{x}{4}}

e^{- 2 x}

2 (25)

e^{- l n (a)}

\frac{( - 5 ) ^{n}}{5 ^{n}}

What is 15/2 x^4y^{-2}(0.13x^5y^4) ?
The solution to 15/2 x^4y^{-2}(0.13x^5y^4) is (39x^9y^2)/(40)