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Popular >

simplify ye^{-2x}*(ye^x)^3

Solution

simplify

y e^{- 2 x} \cdot (y e^{x})^{3}

Solution

e^{x} y^{4}

Solution steps

y e^{- 2 x} (y e^{x})^{3}

Apply exponent rule:

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

= \frac{1}{e ^{2 x}} y (e^{x} y)^{3}

(y e^{x})^{3} : y^{3} e^{3 x}

= y \frac{1}{e ^{2 x}} y^{3} e^{3 x}

Apply exponent rule:

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

y y^{3} = y^{1 + 3}

= \frac{1}{e ^{2 x}} y^{1 + 3} e^{3 x}

Add the numbers:

1 + 3 = 4

= \frac{1}{e ^{2 x}} y^{4} e^{3 x}

Multiply fractions:

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

= \frac{1 \cdot y ^{4} e ^{3 x}}{e ^{2 x}}

Multiply:

1 \cdot y^{4} = y^{4}

= \frac{e ^{3 x} y ^{4}}{e ^{2 x}}

Apply exponent rule:

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

\frac{e ^{3 x}}{e ^{2 x}} = e^{3 x - 2 x} = e^{x}

= e^{x} y^{4}

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Frequently Asked Questions (FAQ)

What is ye^{-2x}*(ye^x)^3 ?
The solution to ye^{-2x}*(ye^x)^3 is e^xy^4